  
  [1X7 [33X[0;0YAdd Functions[133X[101X
  
  [33X[0;0YThis  section  describes  the  overall  structure  of  Add-functions and the
  functions installed by them.[133X
  
  
  [1X7.1 [33X[0;0YFunctions Installed by Add[133X[101X
  
  [33X[0;0YAdd functions have the following syntax:[133X
  
  [4X[32X  Code  [32X[104X
    [4XDeclareOperation( "AddSomeFunc",[104X
    [4X                  [ IsCapCategory, IsList, IsInt ] );[104X
  [4X[32X[104X
  
  [33X[0;0YThe   first   argument   is  the  category  to  which  some  function  (e.g.
  [10XKernelObject[110X)  is  added, the second is a list containing pairs of functions
  and  additional  filters  for  the  arguments,  (e.g.  if  one argument is a
  morphism,  an  additional  filter  could be [10XIsMomomorphism[110X). The third is an
  optional  weight  which will then be the weight for [10XSomeFunc[110X (default value:
  100).  This is described later. If only one function is to be installed, the
  list  can be replaced by the function. CAP installs the given function(s) as
  methods for [10XSomeFunc[110X (resp. [10XSomeFuncOp[110X if [10XSomeFunc[110X is not an operation).[133X
  
  [33X[0;0YAll installed methods follow the following steps, described below:[133X
  
  [30X    [33X[0;6YRedirect function[133X
  
  [30X    [33X[0;6YPrefunction[133X
  
  [30X    [33X[0;6YFunction[133X
  
  [30X    [33X[0;6YLogic[133X
  
  [30X    [33X[0;6YPostfunction[133X
  
  [30X    [33X[0;6YAddfunction[133X
  
  [33X[0;0YEvery  other  part,  except  from  function,  does  only  depend on the name
  [10XSomeFunc[110X. We now explain the steps in detail.[133X
  
  [30X    [33X[0;6YRedirect  function:  The  redirect is used to redirect the computation
        from the given functions to some other symbol. If there is for example
        a  with  given  method  for some universal property, and the universal
        object  is already computed, the redirect function might detect such a
        thing,  calls  the  with  given operation with the universal object as
        additional  argument  and  then  returns  the  value.  In general, the
        redirect  can  be  an  arbitrary  function. It is called with the same
        arguments  as  the  operation  [10XSomeFunc[110X itself and can return an array
        containing  [10X[ true, something ][110X, which will cause the installed method
        to  simply return the object [10Xsomething[110X, or [10X[ false ][110X. If the output is
        [10Xfalse[110X, the computation will continue with the step Prefunction.[133X
  
  [30X    [33X[0;6YPrefunction:  The  prefunction  should  be used for error handling and
        plausibility  checks  of the input to [10XSomeFunc[110X (e.g. for [10XKernelLift[110X it
        should  check  wether  range  and  source  of  the morphims coincide).
        Generally,  the  prefunction  is defined in the method record and only
        depends  on the name [10XSomeFunc[110X. It is called with the same input as the
        function  itself,  and  should return either [10X[ true ][110X, which continues
        the  computation,  or  [10X[ false, "message" ][110X, which will cause an error
        with message [10X"message"[110X and some additional information.[133X
  
  [30X    [33X[0;6YFull  prefunction:  The  full prefuction has the same semantics as the
        prefunction,  but can perform additional, very costly checks. They are
        disabled by default.[133X
  
  [30X    [33X[0;6YFunction:  This  will  launch  the function(s) given as arguments. The
        result  should  be as specified in the type of [10XSomeFunc[110X. The resulting
        object is now named the result.[133X
  
  [30X    [33X[0;6YLogic:  For every function, some logical todos can be implemented in a
        logic texfile for the category. If there is some logic written down in
        a  file  belonging  to  the  category,  or  belonging  to some type of
        category.  Please  see  the  description of logic for more details. If
        there  is  some  logic  and  some predicate relations for the function
        [10XSomeFunc[110X, it is installed in this step for the result.[133X
  
  [30X    [33X[0;6YPostfunction:  The  postfunction  called  with  the  arguments  of the
        function  and  the  result. It can be an arbitrary function doing some
        cosmetics. If for example [10XSomeFunc[110X is [10XKernelEmbedding[110X, it will set the
        [10XKernelObject[110X of the input morphism to result. The postfunction is also
        taken  from  the  method  record  and  does  only  depend  on the name
        [10XSomeFunc[110X.[133X
  
  [30X    [33X[0;6YAddfunction:  If  the  result  is  a category cell, it is added to the
        category  for  which  the  function was installed. This is disabled by
        default  and  can  be  enabled  via  [2XEnableAddForCategoricalOperations[102X
        ([14X1.12-1[114X).[133X
  
  
  [1X7.2 [33X[0;0YAdd Method[133X[101X
  
  [33X[0;0YExcept  from  installing  a  new method for the name [10XSomeFunc[110X, an Add method
  does  slightly  more.  Every Add method has the same structure. The steps in
  the Add method are as follows:[133X
  
  [30X    [33X[0;6YDefault  weight:  If the weight parameter is -1, the default weight is
        assumed, which is 100.[133X
  
  [30X    [33X[0;6YWeight check: If the current weight of the operation is lower than the
        given  weight  of the new functions, then the add function returns and
        installs nothing.[133X
  
  [30X    [33X[0;6YInstallation: Next, the method to install the functions is created. It
        creates  the  correct filter list, by merging the standard filters for
        the  operation  with  the  particular filters for the given functions,
        then installs the method as described above.[133X
  
  [33X[0;0YAfter calling an add method, the corresponding operation is available in the
  category.  Also, some derivations, which are triggered by the setting of the
  primitive value, might be available.[133X
  
  
  [1X7.3 [33X[0;0YInstallAdd Function[133X[101X
  
  [33X[0;0YAlmost   all   Add   methods   in  the  CAP  kernel  are  installed  by  the
  [10XCapInternalInstallAdd[110X  operation.  The  definition  of  this  function is as
  follows:[133X
  
  [4X[32X  Code  [32X[104X
    [4XDeclareOperation( "CapInternalInstallAdd",[104X
    [4X                  [ IsRecord ] );[104X
  [4X[32X[104X
  
  [33X[0;0YThe  record  can  have the following components, most of which can be set in
  the method name record, used as described:[133X
  
  [30X    [33X[0;6Yfunction_name:  The  name  of  the  function.  This  does  not have to
        coincide  with  the  installation  name. It is used for the derivation
        weight.[133X
  
  [30X    [33X[0;6Yinstallation_name  (optional):  A  string  which  is  the  name of the
        operation  for  which  the  functions  given  to  the  Add  method are
        installed as methods.[133X
  
  [30X    [33X[0;6Ypre_function  (optional):  A function which is used as the prefunction
        of  the installed methods, as described above. Can also be the name of
        another  operation.  In  this  case the pre function of the referenced
        operation is used.[133X
  
  [30X    [33X[0;6Ypre_function_full  (optional):  A  function  which is used as the full
        prefunction  of the installed methods, as described above. Can also be
        the  name  of another operation. In this case the full pre function of
        the referenced operation is used.[133X
  
  [30X    [33X[0;6Yredirect_function (optional): A function which is used as the redirect
        function of the installed methods, as described above. Can also be the
        name  of  another operation. In this case the redirect function of the
        referenced operation is used.[133X
  
  [30X    [33X[0;6Ypost_function (optional): A function which is used as the postfunction
        of the installed methods, as described above.[133X
  
  [30X    [33X[0;6Yfilter_list:  A  list  containing  the  basic  filters for the methods
        installed  by  the  add  methods. Possible entries are filters, or the
        strings listed below, which will be replaced by appropriate filters at
        the time the add method is called. The first entry of [10Xfilter_list[110X must
        be  the  string  [10Xcategory[110X.  If  the  category can be inferred from the
        remaining  arguments, a convenience method without the category as the
        first  argument is installed automatically. Additionally, the category
        is   not   passed   to   primitively   added   functions,   except  if
        [10Xcategory!.category_as_first_argument[110X   is   set  to  [10Xtrue[110X  (this  will
        probably change to be the default in the future).[133X
  
        [30X    [33X[0;12Y[10Xcategory[110X,[133X
  
        [30X    [33X[0;12Y[10Xobject[110X,[133X
  
        [30X    [33X[0;12Y[10Xmorphism[110X,[133X
  
        [30X    [33X[0;12Y[10Xtwocell[110X,[133X
  
        [30X    [33X[0;12Y[10Xobject_in_range_category_of_homomorphism_structure[110X,[133X
  
        [30X    [33X[0;12Y[10Xmorphism_in_range_category_of_homomorphism_structure[110X,[133X
  
        [30X    [33X[0;12Y[10Xother_category[110X,[133X
  
        [30X    [33X[0;12Y[10Xother_object[110X,[133X
  
        [30X    [33X[0;12Y[10Xother_morphism[110X,[133X
  
        [30X    [33X[0;12Y[10Xother_twocell[110X,[133X
  
        [30X    [33X[0;12Y[10Xlist_of_objects[110X,[133X
  
        [30X    [33X[0;12Y[10Xlist_of_morphisms[110X,[133X
  
        [30X    [33X[0;12Y[10Xlist_of_twocells[110X.[133X
  
  [30X    [33X[0;6Ywell_defined_todo  (optional): A boolean, default value is true, which
        states  wether there should be to do list entries which propagate well
        definedness  from  the input of the installed methods to their output.
        Please  note  that  true only makes sense if at least one argument and
        the output of the installed method is a cell.[133X
  
  [30X    [33X[0;6Yreturn_type:  The  return  type  can  either be a filter or one of the
        strings  in  the  list  below.  For objects, morphisms and [23X2[123X-cells the
        correct  [10XAdd[110X  function  (see  above)  is  used  for  the result of the
        computation. Otherwise, no [10XAdd[110X function is used after all.[133X
  
  [4X[32X  Code  [32X[104X
    [4X    [[104X
    [4X        "object",[104X
    [4X        "object_or_fail",[104X
    [4X        "morphism",[104X
    [4X        "morphism_or_fail",[104X
    [4X        "twocell",[104X
    [4X        "object_in_range_category_of_homomorphism_structure",[104X
    [4X        "morphism_in_range_category_of_homomorphism_structure",[104X
    [4X        "bool",[104X
    [4X        "other_object",[104X
    [4X        "other_morphism",[104X
    [4X        "list_of_objects",[104X
    [4X        "list_of_morphisms",[104X
    [4X        "list_of_morphisms_or_fail",[104X
    [4X        "object_datum",[104X
    [4X        "morphism_datum",[104X
    [4X        "nonneg_integer_or_infinity",[104X
    [4X    ][104X
  [4X[32X[104X
  
  [30X    [33X[0;6Yis_with_given (optional): Boolean, marks whether the function which is
        to be installed is a with given function or not.[133X
  
  [30X    [33X[0;6Ywith_given_without_given_name_pair   (optional):   If   the  currently
        installed operation has a corresponding with given operation or is the
        with  given  of another operation, the names of both should be in this
        list.[133X
  
  [30X    [33X[0;6Yfunctorial  (optional):  If  an  object has a corresponding functorial
        function,  e.g.,  [10XKernelObject[110X and [10XKernelObjectFunctorial[110X, the name of
        the functorial is stored as a string.[133X
  
  [30X    [33X[0;6Ydual_arguments_reversed  (optional):  Boolean,  marks  whether for the
        call  of the dual operation all arguments have to be given in reversed
        order.[133X
  
  [30X    [33X[0;6Ydual_with_given_arguments_reversed  (optional): Boolean, marks whether
        for  the  call  of  the  dual operation the source and range of a with
        given operation have to be given in reversed order.[133X
  
  [30X    [33X[0;6Ydual_preprocessor_func  (optional):  let  f  be an operation with dual
        operation g. For the automatic installation of g from f, the arguments
        given to g are preprocessed by this given function.[133X
  
  [30X    [33X[0;6Ydual_postprocessor_func  (optional):  let  f be an operation with dual
        operation  g. For the automatic installation of g from f, the computed
        value of f is postprocessed by the given function.[133X
  
  [30X    [33X[0;6Yinput_arguments_names  (optional):  A duplicate free list (of the same
        length  as [10Xfilter_list[110X) of strings. For example, these strings will be
        used  as  the  names  of  the  arguments when automatically generating
        functions for this operation, e.g. in the opposite category.[133X
  
  [30X    [33X[0;6Youtput_source_getter_string  (optional):  Only  valid if the operation
        returns  a  morphism: a piece of GAP code which computes the source of
        the returned morphism. The input arguments are available via the names
        given in [10Xinput_arguments_names[110X.[133X
  
  [30X    [33X[0;6Ycan_always_compute_output_source_getter   (optional):  Only  valid  if
        [10Xoutput_source_getter_string[110X   is   also   set:  Whether  the  code  in
        [10Xoutput_source_getter_string[110X  is  independent of CAP operations and can
        thus  always  be  computed  without  having  to  check  the  installed
        operations of a category.[133X
  
  [30X    [33X[0;6Youtput_range_getter_string  (optional):  Only  valid  if the operation
        returns  a  morphism:  a piece of GAP code which computes the range of
        the returned morphism. The input arguments are available via the names
        given in [10Xinput_arguments_names[110X.[133X
  
  [30X    [33X[0;6Ycan_always_compute_output_range_getter   (optional):   Only  valid  if
        [10Xoutput_range_getter_string[110X   is   also   set:   Whether  the  code  in
        [10Xoutput_range_getter_string[110X  is  independent  of CAP operations and can
        thus  always  be  computed  without  having  to  check  the  installed
        operations of a category.[133X
  
  [30X    [33X[0;6Ywith_given_object_position  (optional):  One of the following strings:
        [10X"Source"[110X, [10X"Range"[110X, or [10X"both"[110X. Set for the without given operation in a
        with  given  pair.  Describes whether the source resp. range are given
        (as  the  last  argument  of the with given operation) or both (as the
        second and the last argument of the with given operation).[133X
  
  [30X    [33X[0;6Ycompatible_with_congruence_of_morphisms  (optional):  Indicates if the
        operation  is compatible with the congruence of morphisms, that is, if
        the  output  does  not  change  with  regard  to [10XIsEqualForObjects[110X and
        [10XIsCongruentForMorphisms[110X   if   the   input   changes  with  regard  to
        [10XIsEqualForObjects[110X and [10XIsCongruentForMorphisms[110X.[133X
  
  [33X[0;0YUsing  all  those  entries, the operation [10XCapInternalInstallAdd[110X installs add
  methods  as  described  above. It first provides plausibility checks for all
  the  entries described, then installs the Add method in 4 ways, with list or
  functions  as  second argument, and with an optional third parameter for the
  weight.[133X
  
  [1X7.3-1 CapInternalInstallAdd[101X
  
  [33X[1;0Y[29X[2XCapInternalInstallAdd[102X( [3Xrecord[103X ) [32X function[133X
  
  [33X[0;0YSee [14X7.3[114X.[133X
  
  
  [1X7.4 [33X[0;0YEnhancing the method name record[133X[101X
  
  [33X[0;0YThe  function  CAP_INTERNAL_ENHANCE_NAME_RECORD  can  be applied to a method
  name record to make the following enhancements:[133X
  
  [30X    [33X[0;6YFunction name: Set the component function_name to the entry name.[133X
  
  [30X    [33X[0;6YWithGiven  special  case:  If the current entry belongs to a WithGiven
        operation      or      its      without      given      pair,      the
        with_given_without_given_name_pair  is  set.  Additionally,  the  with
        given flag of the WithGiven operation is set to true.[133X
  
  [30X    [33X[0;6YRedirect  and  post functions are created for all operations belonging
        to universal constructions (e.g. [10XKernelLift[110X) which are not a WithGiven
        operation.[133X
  
  
  [1X7.5 [33X[0;0YPrepare functions[133X[101X
  
  [1X7.5-1 CAPOperationPrepareFunction[101X
  
  [33X[1;0Y[29X[2XCAPOperationPrepareFunction[102X( [3Xprepare_function[103X, [3Xcategory[103X, [3Xfunc[103X ) [32X function[133X
  [6XReturns:[106X  [33X[0;10Ya function[133X
  
  [33X[0;0YGiven  a  non-CAP-conform  function  for  any of the categorical operations,
  i.e.,  a  function  that computes the direct sum of two objects instead of a
  list of objects, this function wraps the function with a wrapper function to
  fit  in  the  CAP  context. For the mentioned binary direct sum one can call
  this  function  with  [10X"BinaryDirectSumToDirectSum"[110X  as [3Xprepare_function[103X, the
  category,  and  the  binary direct sum function. The function then returns a
  function that can be used for the direct sum categorical operation.[133X
  
  [33X[0;0YNote  that [3Xfunc[103X is not handled by the CAP caching mechanism and that the use
  of  prepare  functions  is incompatible with [10XWithGiven[110X operations. Thus, one
  has  to  ensure  manually  that  the  equality and typing specifications are
  fulfilled.[133X
  
  [1X7.5-2 CAPAddPrepareFunction[101X
  
  [33X[1;0Y[29X[2XCAPAddPrepareFunction[102X( [3Xprepare_function[103X, [3Xname[103X, [3Xdoc_string[103X[, [3Xprecondition_list[103X] ) [32X function[133X
  
  [33X[0;0YAdds  a  prepare  function to the list of CAP's prepare functions. The first
  argument is the prepare function itself. It should always be a function that
  takes a category and a function and returns a function. The argument [3Xname[103X is
  the    name    of    the    prepare    function,    which    is    used   in
  [10XCAPOperationPrepareFunction[110X.  The  argument  [3Xdoc_string[103X  should  be  a short
  string describing the functions. The optional argument [3Xprecondition_list[103X can
  describe  preconditions  for  the  prepare  function  to  work, i.e., if the
  category  does  need to have PreCompose computable. This information is also
  recovered   automatically   from   the   prepare  function  itself,  so  the
  [3Xprecondition_list[103X is only necessary if the function needed is not explicitly
  used   in   the   prepare   function,   e.g.,   if  you  use  [10X+[110X  instead  of
  [10XAdditionForMorphisms[110X.[133X
  
  [1X7.5-3 ListCAPPrepareFunctions[101X
  
  [33X[1;0Y[29X[2XListCAPPrepareFunctions[102X( [3Xarg[103X ) [32X function[133X
  
  [33X[0;0YLists all prepare functions.[133X
  
  
  [1X7.6 [33X[0;0YAvailable Add functions[133X[101X
  
  [1X7.6-1 AddAdditionForMorphisms[101X
  
  [33X[1;0Y[29X[2XAddAdditionForMorphisms[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XAdditionForMorphisms[110X.  [23XF:  ( a, b ) \mapsto \mathtt{AdditionForMorphisms}(a,
  b)[123X.[133X
  
  [1X7.6-2 AddAdditiveGenerators[101X
  
  [33X[1;0Y[29X[2XAddAdditiveGenerators[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given function [23XF[123X to the category for the basic operation [10XAdditiveGenerators[110X.
  [23XF: ( ) \mapsto \mathtt{AdditiveGenerators}()[123X.[133X
  
  [1X7.6-3 AddAdditiveInverseForMorphisms[101X
  
  [33X[1;0Y[29X[2XAddAdditiveInverseForMorphisms[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XAdditiveInverseForMorphisms[110X.        [23XF:       (       a       )       \mapsto
  \mathtt{AdditiveInverseForMorphisms}(a)[123X.[133X
  
  [1X7.6-4 AddAstrictionToCoimage[101X
  
  [33X[1;0Y[29X[2XAddAstrictionToCoimage[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XAstrictionToCoimage[110X.        [23XF:        (        alpha        )        \mapsto
  \mathtt{AstrictionToCoimage}(alpha)[123X.[133X
  
  [1X7.6-5 AddAstrictionToCoimageWithGivenCoimageObject[101X
  
  [33X[1;0Y[29X[2XAddAstrictionToCoimageWithGivenCoimageObject[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XAstrictionToCoimageWithGivenCoimageObject[110X.   [23XF:   (   alpha,   C  )  \mapsto
  \mathtt{AstrictionToCoimageWithGivenCoimageObject}(alpha, C)[123X.[133X
  
  [1X7.6-6 AddBasisOfExternalHom[101X
  
  [33X[1;0Y[29X[2XAddBasisOfExternalHom[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given function [23XF[123X to the category for the basic operation [10XBasisOfExternalHom[110X.
  [23XF: ( arg2, arg3 ) \mapsto \mathtt{BasisOfExternalHom}(arg2, arg3)[123X.[133X
  
  [1X7.6-7 AddCanonicalIdentificationFromCoimageToImageObject[101X
  
  [33X[1;0Y[29X[2XAddCanonicalIdentificationFromCoimageToImageObject[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XCanonicalIdentificationFromCoimageToImageObject[110X.   [23XF:   (  alpha  )  \mapsto
  \mathtt{CanonicalIdentificationFromCoimageToImageObject}(alpha)[123X.[133X
  
  [1X7.6-8 AddCanonicalIdentificationFromImageObjectToCoimage[101X
  
  [33X[1;0Y[29X[2XAddCanonicalIdentificationFromImageObjectToCoimage[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XCanonicalIdentificationFromImageObjectToCoimage[110X.   [23XF:   (  alpha  )  \mapsto
  \mathtt{CanonicalIdentificationFromImageObjectToCoimage}(alpha)[123X.[133X
  
  [1X7.6-9 AddCoastrictionToImage[101X
  
  [33X[1;0Y[29X[2XAddCoastrictionToImage[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XCoastrictionToImage[110X.        [23XF:        (        alpha        )        \mapsto
  \mathtt{CoastrictionToImage}(alpha)[123X.[133X
  
  [1X7.6-10 AddCoastrictionToImageWithGivenImageObject[101X
  
  [33X[1;0Y[29X[2XAddCoastrictionToImageWithGivenImageObject[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XCoastrictionToImageWithGivenImageObject[110X.   [23XF:   (   alpha,   I   )   \mapsto
  \mathtt{CoastrictionToImageWithGivenImageObject}(alpha, I)[123X.[133X
  
  [1X7.6-11 AddCoefficientsOfMorphism[101X
  
  [33X[1;0Y[29X[2XAddCoefficientsOfMorphism[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XCoefficientsOfMorphism[110X.        [23XF:        (        arg2       )       \mapsto
  \mathtt{CoefficientsOfMorphism}(arg2)[123X.[133X
  
  [1X7.6-12 AddCoequalizer[101X
  
  [33X[1;0Y[29X[2XAddCoequalizer[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given  function  [23XF[123X to the category for the basic operation [10XCoequalizer[110X. [23XF: (
  arg2, arg3 ) \mapsto \mathtt{Coequalizer}(arg2, arg3)[123X.[133X
  
  [1X7.6-13 AddCoequalizerFunctorial[101X
  
  [33X[1;0Y[29X[2XAddCoequalizerFunctorial[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XCoequalizerFunctorial[110X.   [23XF:   (   morphisms,   mu,   morphismsp   )  \mapsto
  \mathtt{CoequalizerFunctorial}(morphisms, mu, morphismsp)[123X.[133X
  
  [1X7.6-14 AddCoequalizerFunctorialWithGivenCoequalizers[101X
  
  [33X[1;0Y[29X[2XAddCoequalizerFunctorialWithGivenCoequalizers[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XCoequalizerFunctorialWithGivenCoequalizers[110X.   [23XF:   (   P,   morphisms,   mu,
  morphismsp,                   Pp                  )                  \mapsto
  \mathtt{CoequalizerFunctorialWithGivenCoequalizers}(P,     morphisms,    mu,
  morphismsp, Pp)[123X.[133X
  
  [1X7.6-15 AddCoimageObject[101X
  
  [33X[1;0Y[29X[2XAddCoimageObject[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given function [23XF[123X to the category for the basic operation [10XCoimageObject[110X. [23XF: (
  arg2 ) \mapsto \mathtt{CoimageObject}(arg2)[123X.[133X
  
  [1X7.6-16 AddCoimageObjectFunctorial[101X
  
  [33X[1;0Y[29X[2XAddCoimageObjectFunctorial[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XCoimageObjectFunctorial[110X.    [23XF:    (    alpha,    mu,    alphap   )   \mapsto
  \mathtt{CoimageObjectFunctorial}(alpha, mu, alphap)[123X.[133X
  
  [1X7.6-17 AddCoimageObjectFunctorialWithGivenCoimageObjects[101X
  
  [33X[1;0Y[29X[2XAddCoimageObjectFunctorialWithGivenCoimageObjects[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XCoimageObjectFunctorialWithGivenCoimageObjects[110X.  [23XF:  ( C, alpha, mu, alphap,
  Cp   )   \mapsto  \mathtt{CoimageObjectFunctorialWithGivenCoimageObjects}(C,
  alpha, mu, alphap, Cp)[123X.[133X
  
  [1X7.6-18 AddCoimageProjection[101X
  
  [33X[1;0Y[29X[2XAddCoimageProjection[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given  function [23XF[123X to the category for the basic operation [10XCoimageProjection[110X.
  [23XF: ( alpha ) \mapsto \mathtt{CoimageProjection}(alpha)[123X.[133X
  
  [1X7.6-19 AddCoimageProjectionWithGivenCoimageObject[101X
  
  [33X[1;0Y[29X[2XAddCoimageProjectionWithGivenCoimageObject[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XCoimageProjectionWithGivenCoimageObject[110X.   [23XF:   (   alpha,   C   )   \mapsto
  \mathtt{CoimageProjectionWithGivenCoimageObject}(alpha, C)[123X.[133X
  
  [1X7.6-20 AddCokernelColift[101X
  
  [33X[1;0Y[29X[2XAddCokernelColift[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given  function [23XF[123X to the category for the basic operation [10XCokernelColift[110X. [23XF:
  ( alpha, T, tau ) \mapsto \mathtt{CokernelColift}(alpha, T, tau)[123X.[133X
  
  [1X7.6-21 AddCokernelColiftWithGivenCokernelObject[101X
  
  [33X[1;0Y[29X[2XAddCokernelColiftWithGivenCokernelObject[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XCokernelColiftWithGivenCokernelObject[110X.  [23XF:  (  alpha,  T,  tau,  P ) \mapsto
  \mathtt{CokernelColiftWithGivenCokernelObject}(alpha, T, tau, P)[123X.[133X
  
  [1X7.6-22 AddCokernelObject[101X
  
  [33X[1;0Y[29X[2XAddCokernelObject[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given  function [23XF[123X to the category for the basic operation [10XCokernelObject[110X. [23XF:
  ( arg2 ) \mapsto \mathtt{CokernelObject}(arg2)[123X.[133X
  
  [1X7.6-23 AddCokernelObjectFunctorial[101X
  
  [33X[1;0Y[29X[2XAddCokernelObjectFunctorial[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XCokernelObjectFunctorial[110X.    [23XF:    (    alpha,    mu,   alphap   )   \mapsto
  \mathtt{CokernelObjectFunctorial}(alpha, mu, alphap)[123X.[133X
  
  [1X7.6-24 AddCokernelObjectFunctorialWithGivenCokernelObjects[101X
  
  [33X[1;0Y[29X[2XAddCokernelObjectFunctorialWithGivenCokernelObjects[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XCokernelObjectFunctorialWithGivenCokernelObjects[110X. [23XF: ( P, alpha, mu, alphap,
  Pp  )  \mapsto  \mathtt{CokernelObjectFunctorialWithGivenCokernelObjects}(P,
  alpha, mu, alphap, Pp)[123X.[133X
  
  [1X7.6-25 AddCokernelProjection[101X
  
  [33X[1;0Y[29X[2XAddCokernelProjection[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given function [23XF[123X to the category for the basic operation [10XCokernelProjection[110X.
  [23XF: ( alpha ) \mapsto \mathtt{CokernelProjection}(alpha)[123X.[133X
  
  [1X7.6-26 AddCokernelProjectionWithGivenCokernelObject[101X
  
  [33X[1;0Y[29X[2XAddCokernelProjectionWithGivenCokernelObject[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XCokernelProjectionWithGivenCokernelObject[110X.   [23XF:   (   alpha,   P  )  \mapsto
  \mathtt{CokernelProjectionWithGivenCokernelObject}(alpha, P)[123X.[133X
  
  [1X7.6-27 AddColift[101X
  
  [33X[1;0Y[29X[2XAddColift[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given function [23XF[123X to the category for the basic operation [10XColift[110X. [23XF: ( alpha,
  beta ) \mapsto \mathtt{Colift}(alpha, beta)[123X.[133X
  
  [1X7.6-28 AddColiftAlongEpimorphism[101X
  
  [33X[1;0Y[29X[2XAddColiftAlongEpimorphism[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XColiftAlongEpimorphism[110X.      [23XF:     (     epsilon,     tau     )     \mapsto
  \mathtt{ColiftAlongEpimorphism}(epsilon, tau)[123X.[133X
  
  [1X7.6-29 AddColiftOrFail[101X
  
  [33X[1;0Y[29X[2XAddColiftOrFail[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given  function [23XF[123X to the category for the basic operation [10XColiftOrFail[110X. [23XF: (
  alpha, beta ) \mapsto \mathtt{ColiftOrFail}(alpha, beta)[123X.[133X
  
  [1X7.6-30 AddComponentOfMorphismFromDirectSum[101X
  
  [33X[1;0Y[29X[2XAddComponentOfMorphismFromDirectSum[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XComponentOfMorphismFromDirectSum[110X.    [23XF:    (   alpha,   S,   i   )   \mapsto
  \mathtt{ComponentOfMorphismFromDirectSum}(alpha, S, i)[123X.[133X
  
  [1X7.6-31 AddComponentOfMorphismIntoDirectSum[101X
  
  [33X[1;0Y[29X[2XAddComponentOfMorphismIntoDirectSum[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XComponentOfMorphismIntoDirectSum[110X.    [23XF:    (   alpha,   S,   i   )   \mapsto
  \mathtt{ComponentOfMorphismIntoDirectSum}(alpha, S, i)[123X.[133X
  
  [1X7.6-32 AddCoproduct[101X
  
  [33X[1;0Y[29X[2XAddCoproduct[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given  function  [23XF[123X  to  the category for the basic operation [10XCoproduct[110X. [23XF: (
  arg2 ) \mapsto \mathtt{Coproduct}(arg2)[123X.[133X
  
  [1X7.6-33 AddCoproductFunctorial[101X
  
  [33X[1;0Y[29X[2XAddCoproductFunctorial[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XCoproductFunctorial[110X.    [23XF:    (    objects,    L,    objectsp    )   \mapsto
  \mathtt{CoproductFunctorial}(objects, L, objectsp)[123X.[133X
  
  [1X7.6-34 AddCoproductFunctorialWithGivenCoproducts[101X
  
  [33X[1;0Y[29X[2XAddCoproductFunctorialWithGivenCoproducts[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XCoproductFunctorialWithGivenCoproducts[110X.  [23XF:  ( P, objects, L, objectsp, Pp )
  \mapsto   \mathtt{CoproductFunctorialWithGivenCoproducts}(P,   objects,   L,
  objectsp, Pp)[123X.[133X
  
  [1X7.6-35 AddDirectProduct[101X
  
  [33X[1;0Y[29X[2XAddDirectProduct[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given function [23XF[123X to the category for the basic operation [10XDirectProduct[110X. [23XF: (
  arg2 ) \mapsto \mathtt{DirectProduct}(arg2)[123X.[133X
  
  [1X7.6-36 AddDirectProductFunctorial[101X
  
  [33X[1;0Y[29X[2XAddDirectProductFunctorial[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XDirectProductFunctorial[110X.    [23XF:    (   objects,   L,   objectsp   )   \mapsto
  \mathtt{DirectProductFunctorial}(objects, L, objectsp)[123X.[133X
  
  [1X7.6-37 AddDirectProductFunctorialWithGivenDirectProducts[101X
  
  [33X[1;0Y[29X[2XAddDirectProductFunctorialWithGivenDirectProducts[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XDirectProductFunctorialWithGivenDirectProducts[110X.   [23XF:   (   P,   objects,  L,
  objectsp,                   Pp                   )                   \mapsto
  \mathtt{DirectProductFunctorialWithGivenDirectProducts}(P,    objects,    L,
  objectsp, Pp)[123X.[133X
  
  [1X7.6-38 AddDirectSum[101X
  
  [33X[1;0Y[29X[2XAddDirectSum[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given  function  [23XF[123X  to  the category for the basic operation [10XDirectSum[110X. [23XF: (
  arg2 ) \mapsto \mathtt{DirectSum}(arg2)[123X.[133X
  
  [1X7.6-39 AddDirectSumCodiagonalDifference[101X
  
  [33X[1;0Y[29X[2XAddDirectSumCodiagonalDifference[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XDirectSumCodiagonalDifference[110X.       [23XF:       (       D       )      \mapsto
  \mathtt{DirectSumCodiagonalDifference}(D)[123X.[133X
  
  [1X7.6-40 AddDirectSumDiagonalDifference[101X
  
  [33X[1;0Y[29X[2XAddDirectSumDiagonalDifference[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XDirectSumDiagonalDifference[110X.        [23XF:       (       D       )       \mapsto
  \mathtt{DirectSumDiagonalDifference}(D)[123X.[133X
  
  [1X7.6-41 AddDirectSumFunctorial[101X
  
  [33X[1;0Y[29X[2XAddDirectSumFunctorial[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XDirectSumFunctorial[110X.    [23XF:    (    objects,    L,    objectsp    )   \mapsto
  \mathtt{DirectSumFunctorial}(objects, L, objectsp)[123X.[133X
  
  [1X7.6-42 AddDirectSumFunctorialWithGivenDirectSums[101X
  
  [33X[1;0Y[29X[2XAddDirectSumFunctorialWithGivenDirectSums[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XDirectSumFunctorialWithGivenDirectSums[110X.  [23XF:  ( P, objects, L, objectsp, Pp )
  \mapsto   \mathtt{DirectSumFunctorialWithGivenDirectSums}(P,   objects,   L,
  objectsp, Pp)[123X.[133X
  
  [1X7.6-43 AddDirectSumProjectionInPushout[101X
  
  [33X[1;0Y[29X[2XAddDirectSumProjectionInPushout[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XDirectSumProjectionInPushout[110X.       [23XF:       (       D       )       \mapsto
  \mathtt{DirectSumProjectionInPushout}(D)[123X.[133X
  
  [1X7.6-44 AddDistinguishedObjectOfHomomorphismStructure[101X
  
  [33X[1;0Y[29X[2XAddDistinguishedObjectOfHomomorphismStructure[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XDistinguishedObjectOfHomomorphismStructure[110X.      [23XF:      (     )     \mapsto
  \mathtt{DistinguishedObjectOfHomomorphismStructure}()[123X.[133X
  
  [1X7.6-45 AddEmbeddingOfEqualizer[101X
  
  [33X[1;0Y[29X[2XAddEmbeddingOfEqualizer[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XEmbeddingOfEqualizer[110X.      [23XF:      (      Y,     morphisms     )     \mapsto
  \mathtt{EmbeddingOfEqualizer}(Y, morphisms)[123X.[133X
  
  [1X7.6-46 AddEmbeddingOfEqualizerWithGivenEqualizer[101X
  
  [33X[1;0Y[29X[2XAddEmbeddingOfEqualizerWithGivenEqualizer[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XEmbeddingOfEqualizerWithGivenEqualizer[110X.  [23XF:  (  Y,  morphisms,  P  ) \mapsto
  \mathtt{EmbeddingOfEqualizerWithGivenEqualizer}(Y, morphisms, P)[123X.[133X
  
  [1X7.6-47 AddEpimorphismFromProjectiveCoverObject[101X
  
  [33X[1;0Y[29X[2XAddEpimorphismFromProjectiveCoverObject[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XEpimorphismFromProjectiveCoverObject[110X.      [23XF:      (     A     )     \mapsto
  \mathtt{EpimorphismFromProjectiveCoverObject}(A)[123X.[133X
  
  [1X7.6-48 AddEpimorphismFromProjectiveCoverObjectWithGivenProjectiveCoverObject[101X
  
  [33X[1;0Y[29X[2XAddEpimorphismFromProjectiveCoverObjectWithGivenProjectiveCoverObject[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XEpimorphismFromProjectiveCoverObjectWithGivenProjectiveCoverObject[110X.  [23XF: ( A,
  P                                  )                                 \mapsto
  \mathtt{EpimorphismFromProjectiveCoverObjectWithGivenProjectiveCoverObject}(A,
  P)[123X.[133X
  
  [1X7.6-49 AddEpimorphismFromSomeProjectiveObject[101X
  
  [33X[1;0Y[29X[2XAddEpimorphismFromSomeProjectiveObject[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XEpimorphismFromSomeProjectiveObject[110X.      [23XF:      (      A     )     \mapsto
  \mathtt{EpimorphismFromSomeProjectiveObject}(A)[123X.[133X
  
  [1X7.6-50 AddEpimorphismFromSomeProjectiveObjectWithGivenSomeProjectiveObject[101X
  
  [33X[1;0Y[29X[2XAddEpimorphismFromSomeProjectiveObjectWithGivenSomeProjectiveObject[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XEpimorphismFromSomeProjectiveObjectWithGivenSomeProjectiveObject[110X.  [23XF: ( A, P
  )                                                                    \mapsto
  \mathtt{EpimorphismFromSomeProjectiveObjectWithGivenSomeProjectiveObject}(A,
  P)[123X.[133X
  
  [1X7.6-51 AddEqualizer[101X
  
  [33X[1;0Y[29X[2XAddEqualizer[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given  function  [23XF[123X  to  the category for the basic operation [10XEqualizer[110X. [23XF: (
  arg2, arg3 ) \mapsto \mathtt{Equalizer}(arg2, arg3)[123X.[133X
  
  [1X7.6-52 AddEqualizerFunctorial[101X
  
  [33X[1;0Y[29X[2XAddEqualizerFunctorial[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XEqualizerFunctorial[110X.    [23XF:   (   morphisms,   mu,   morphismsp   )   \mapsto
  \mathtt{EqualizerFunctorial}(morphisms, mu, morphismsp)[123X.[133X
  
  [1X7.6-53 AddEqualizerFunctorialWithGivenEqualizers[101X
  
  [33X[1;0Y[29X[2XAddEqualizerFunctorialWithGivenEqualizers[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XEqualizerFunctorialWithGivenEqualizers[110X.  [23XF:  ( P, morphisms, mu, morphismsp,
  Pp  )  \mapsto \mathtt{EqualizerFunctorialWithGivenEqualizers}(P, morphisms,
  mu, morphismsp, Pp)[123X.[133X
  
  [1X7.6-54 AddFiberProduct[101X
  
  [33X[1;0Y[29X[2XAddFiberProduct[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given  function [23XF[123X to the category for the basic operation [10XFiberProduct[110X. [23XF: (
  arg2 ) \mapsto \mathtt{FiberProduct}(arg2)[123X.[133X
  
  [1X7.6-55 AddFiberProductEmbeddingInDirectSum[101X
  
  [33X[1;0Y[29X[2XAddFiberProductEmbeddingInDirectSum[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XFiberProductEmbeddingInDirectSum[110X.       [23XF:      (      D      )      \mapsto
  \mathtt{FiberProductEmbeddingInDirectSum}(D)[123X.[133X
  
  [1X7.6-56 AddFiberProductFunctorial[101X
  
  [33X[1;0Y[29X[2XAddFiberProductFunctorial[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XFiberProductFunctorial[110X.   [23XF:   (   morphisms,   L,   morphismsp   )  \mapsto
  \mathtt{FiberProductFunctorial}(morphisms, L, morphismsp)[123X.[133X
  
  [1X7.6-57 AddFiberProductFunctorialWithGivenFiberProducts[101X
  
  [33X[1;0Y[29X[2XAddFiberProductFunctorialWithGivenFiberProducts[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XFiberProductFunctorialWithGivenFiberProducts[110X.   [23XF:   (   P,   morphisms,  L,
  morphismsp,                   Pp                  )                  \mapsto
  \mathtt{FiberProductFunctorialWithGivenFiberProducts}(P,    morphisms,    L,
  morphismsp, Pp)[123X.[133X
  
  [1X7.6-58 AddHomologyObject[101X
  
  [33X[1;0Y[29X[2XAddHomologyObject[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given  function [23XF[123X to the category for the basic operation [10XHomologyObject[110X. [23XF:
  ( alpha, beta ) \mapsto \mathtt{HomologyObject}(alpha, beta)[123X.[133X
  
  [1X7.6-59 AddHomologyObjectFunctorialWithGivenHomologyObjects[101X
  
  [33X[1;0Y[29X[2XAddHomologyObjectFunctorialWithGivenHomologyObjects[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XHomologyObjectFunctorialWithGivenHomologyObjects[110X. [23XF: ( H_1, L, H_2 ) \mapsto
  \mathtt{HomologyObjectFunctorialWithGivenHomologyObjects}(H_1, L, H_2)[123X.[133X
  
  [1X7.6-60 AddHomomorphismStructureOnMorphisms[101X
  
  [33X[1;0Y[29X[2XAddHomomorphismStructureOnMorphisms[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XHomomorphismStructureOnMorphisms[110X.    [23XF:    (    alpha,    beta   )   \mapsto
  \mathtt{HomomorphismStructureOnMorphisms}(alpha, beta)[123X.[133X
  
  [1X7.6-61 AddHomomorphismStructureOnMorphismsWithGivenObjects[101X
  
  [33X[1;0Y[29X[2XAddHomomorphismStructureOnMorphismsWithGivenObjects[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XHomomorphismStructureOnMorphismsWithGivenObjects[110X.  [23XF: ( source, alpha, beta,
  range                                )                               \mapsto
  \mathtt{HomomorphismStructureOnMorphismsWithGivenObjects}(source,     alpha,
  beta, range)[123X.[133X
  
  [1X7.6-62 AddHomomorphismStructureOnObjects[101X
  
  [33X[1;0Y[29X[2XAddHomomorphismStructureOnObjects[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XHomomorphismStructureOnObjects[110X.     [23XF:    (    arg2,    arg3    )    \mapsto
  \mathtt{HomomorphismStructureOnObjects}(arg2, arg3)[123X.[133X
  
  [1X7.6-63 AddHorizontalPostCompose[101X
  
  [33X[1;0Y[29X[2XAddHorizontalPostCompose[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XHorizontalPostCompose[110X.      [23XF:      (      arg2,      arg3     )     \mapsto
  \mathtt{HorizontalPostCompose}(arg2, arg3)[123X.[133X
  
  [1X7.6-64 AddHorizontalPreCompose[101X
  
  [33X[1;0Y[29X[2XAddHorizontalPreCompose[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XHorizontalPreCompose[110X.      [23XF:      (      arg2,      arg3      )     \mapsto
  \mathtt{HorizontalPreCompose}(arg2, arg3)[123X.[133X
  
  [1X7.6-65 AddIdentityMorphism[101X
  
  [33X[1;0Y[29X[2XAddIdentityMorphism[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given  function  [23XF[123X to the category for the basic operation [10XIdentityMorphism[110X.
  [23XF: ( a ) \mapsto \mathtt{IdentityMorphism}(a)[123X.[133X
  
  [1X7.6-66 AddIdentityTwoCell[101X
  
  [33X[1;0Y[29X[2XAddIdentityTwoCell[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given function [23XF[123X to the category for the basic operation [10XIdentityTwoCell[110X. [23XF:
  ( arg2 ) \mapsto \mathtt{IdentityTwoCell}(arg2)[123X.[133X
  
  [1X7.6-67 AddImageEmbedding[101X
  
  [33X[1;0Y[29X[2XAddImageEmbedding[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given  function [23XF[123X to the category for the basic operation [10XImageEmbedding[110X. [23XF:
  ( alpha ) \mapsto \mathtt{ImageEmbedding}(alpha)[123X.[133X
  
  [1X7.6-68 AddImageEmbeddingWithGivenImageObject[101X
  
  [33X[1;0Y[29X[2XAddImageEmbeddingWithGivenImageObject[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XImageEmbeddingWithGivenImageObject[110X.    [23XF:    (    alpha,    I    )   \mapsto
  \mathtt{ImageEmbeddingWithGivenImageObject}(alpha, I)[123X.[133X
  
  [1X7.6-69 AddImageObject[101X
  
  [33X[1;0Y[29X[2XAddImageObject[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given  function  [23XF[123X to the category for the basic operation [10XImageObject[110X. [23XF: (
  arg2 ) \mapsto \mathtt{ImageObject}(arg2)[123X.[133X
  
  [1X7.6-70 AddImageObjectFunctorial[101X
  
  [33X[1;0Y[29X[2XAddImageObjectFunctorial[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XImageObjectFunctorial[110X.    [23XF:    (    alpha,    nu,    alphap    )    \mapsto
  \mathtt{ImageObjectFunctorial}(alpha, nu, alphap)[123X.[133X
  
  [1X7.6-71 AddImageObjectFunctorialWithGivenImageObjects[101X
  
  [33X[1;0Y[29X[2XAddImageObjectFunctorialWithGivenImageObjects[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XImageObjectFunctorialWithGivenImageObjects[110X.  [23XF: ( I, alpha, nu, alphap, Ip )
  \mapsto  \mathtt{ImageObjectFunctorialWithGivenImageObjects}(I,  alpha,  nu,
  alphap, Ip)[123X.[133X
  
  [1X7.6-72 AddIndecomposableInjectiveObjects[101X
  
  [33X[1;0Y[29X[2XAddIndecomposableInjectiveObjects[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XIndecomposableInjectiveObjects[110X.         [23XF:         (        )        \mapsto
  \mathtt{IndecomposableInjectiveObjects}()[123X.[133X
  
  [1X7.6-73 AddIndecomposableProjectiveObjects[101X
  
  [33X[1;0Y[29X[2XAddIndecomposableProjectiveObjects[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XIndecomposableProjectiveObjects[110X.         [23XF:        (        )        \mapsto
  \mathtt{IndecomposableProjectiveObjects}()[123X.[133X
  
  [1X7.6-74 AddInitialObject[101X
  
  [33X[1;0Y[29X[2XAddInitialObject[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given function [23XF[123X to the category for the basic operation [10XInitialObject[110X. [23XF: (
  ) \mapsto \mathtt{InitialObject}()[123X.[133X
  
  [1X7.6-75 AddInitialObjectFunctorial[101X
  
  [33X[1;0Y[29X[2XAddInitialObjectFunctorial[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XInitialObjectFunctorial[110X. [23XF: ( ) \mapsto \mathtt{InitialObjectFunctorial}()[123X.[133X
  
  [1X7.6-76 AddInitialObjectFunctorialWithGivenInitialObjects[101X
  
  [33X[1;0Y[29X[2XAddInitialObjectFunctorialWithGivenInitialObjects[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XInitialObjectFunctorialWithGivenInitialObjects[110X.   [23XF:   (  P,  Pp  )  \mapsto
  \mathtt{InitialObjectFunctorialWithGivenInitialObjects}(P, Pp)[123X.[133X
  
  [1X7.6-77 AddInjectionOfCofactorOfCoproduct[101X
  
  [33X[1;0Y[29X[2XAddInjectionOfCofactorOfCoproduct[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XInjectionOfCofactorOfCoproduct[110X.     [23XF:    (    objects,    k    )    \mapsto
  \mathtt{InjectionOfCofactorOfCoproduct}(objects, k)[123X.[133X
  
  [1X7.6-78 AddInjectionOfCofactorOfCoproductWithGivenCoproduct[101X
  
  [33X[1;0Y[29X[2XAddInjectionOfCofactorOfCoproductWithGivenCoproduct[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XInjectionOfCofactorOfCoproductWithGivenCoproduct[110X.  [23XF:  (  objects,  k,  P  )
  \mapsto   \mathtt{InjectionOfCofactorOfCoproductWithGivenCoproduct}(objects,
  k, P)[123X.[133X
  
  [1X7.6-79 AddInjectionOfCofactorOfDirectSum[101X
  
  [33X[1;0Y[29X[2XAddInjectionOfCofactorOfDirectSum[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XInjectionOfCofactorOfDirectSum[110X.     [23XF:    (    objects,    k    )    \mapsto
  \mathtt{InjectionOfCofactorOfDirectSum}(objects, k)[123X.[133X
  
  [1X7.6-80 AddInjectionOfCofactorOfDirectSumWithGivenDirectSum[101X
  
  [33X[1;0Y[29X[2XAddInjectionOfCofactorOfDirectSumWithGivenDirectSum[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XInjectionOfCofactorOfDirectSumWithGivenDirectSum[110X.  [23XF:  (  objects,  k,  P  )
  \mapsto   \mathtt{InjectionOfCofactorOfDirectSumWithGivenDirectSum}(objects,
  k, P)[123X.[133X
  
  [1X7.6-81 AddInjectionOfCofactorOfPushout[101X
  
  [33X[1;0Y[29X[2XAddInjectionOfCofactorOfPushout[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XInjectionOfCofactorOfPushout[110X.     [23XF:    (    morphisms,    k    )    \mapsto
  \mathtt{InjectionOfCofactorOfPushout}(morphisms, k)[123X.[133X
  
  [1X7.6-82 AddInjectionOfCofactorOfPushoutWithGivenPushout[101X
  
  [33X[1;0Y[29X[2XAddInjectionOfCofactorOfPushoutWithGivenPushout[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XInjectionOfCofactorOfPushoutWithGivenPushout[110X. [23XF: ( morphisms, k, P ) \mapsto
  \mathtt{InjectionOfCofactorOfPushoutWithGivenPushout}(morphisms, k, P)[123X.[133X
  
  [1X7.6-83 AddInjectiveColift[101X
  
  [33X[1;0Y[29X[2XAddInjectiveColift[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given function [23XF[123X to the category for the basic operation [10XInjectiveColift[110X. [23XF:
  ( alpha, beta ) \mapsto \mathtt{InjectiveColift}(alpha, beta)[123X.[133X
  
  [1X7.6-84 AddInjectiveDimension[101X
  
  [33X[1;0Y[29X[2XAddInjectiveDimension[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given function [23XF[123X to the category for the basic operation [10XInjectiveDimension[110X.
  [23XF: ( arg2 ) \mapsto \mathtt{InjectiveDimension}(arg2)[123X.[133X
  
  [1X7.6-85 AddInjectiveEnvelopeObject[101X
  
  [33X[1;0Y[29X[2XAddInjectiveEnvelopeObject[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XInjectiveEnvelopeObject[110X.        [23XF:        (       arg2       )       \mapsto
  \mathtt{InjectiveEnvelopeObject}(arg2)[123X.[133X
  
  [1X7.6-86 AddInterpretMorphismAsMorphismFromDistinguishedObjectToHomomorphismStructure[101X
  
  [33X[1;0Y[29X[2XAddInterpretMorphismAsMorphismFromDistinguishedObjectToHomomorphismStructure[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XInterpretMorphismAsMorphismFromDistinguishedObjectToHomomorphismStructure[110X.
  [23XF:               (               alpha               )               \mapsto
  \mathtt{InterpretMorphismAsMorphismFromDistinguishedObjectToHomomorphismStructure}(alpha)
  .[133X
  
  [1X7.6-87 AddInterpretMorphismAsMorphismFromDistinguishedObjectToHomomorphismStructureWithGivenObjects[101X
  
  [33X[1;0Y[29X[2XAddInterpretMorphismAsMorphismFromDistinguishedObjectToHomomorphismStructureWithGivenObjects[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XInterpretMorphismAsMorphismFromDistinguishedObjectToHomomorphismStructureWithGivenObjects[110X.
  [23XF:        (        source,        alpha,        range        )       \mapsto
  \mathtt{InterpretMorphismAsMorphismFromDistinguishedObjectToHomomorphismStructureWithGivenObjects}(source,
  alpha, range)[123X.[133X
  
  [1X7.6-88 AddInterpretMorphismFromDistinguishedObjectToHomomorphismStructureAsMorphism[101X
  
  [33X[1;0Y[29X[2XAddInterpretMorphismFromDistinguishedObjectToHomomorphismStructureAsMorphism[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XInterpretMorphismFromDistinguishedObjectToHomomorphismStructureAsMorphism[110X.
  [23XF:        (        source,        range,        alpha        )       \mapsto
  \mathtt{InterpretMorphismFromDistinguishedObjectToHomomorphismStructureAsMorphism}(source,
  range, alpha)[123X.[133X
  
  [1X7.6-89 AddInverseForMorphisms[101X
  
  [33X[1;0Y[29X[2XAddInverseForMorphisms[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XInverseForMorphisms[110X.        [23XF:        (        alpha        )        \mapsto
  \mathtt{InverseForMorphisms}(alpha)[123X.[133X
  
  [1X7.6-90 AddInverseMorphismFromCoimageToImageWithGivenObjects[101X
  
  [33X[1;0Y[29X[2XAddInverseMorphismFromCoimageToImageWithGivenObjects[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XInverseMorphismFromCoimageToImageWithGivenObjects[110X.   [23XF:  (  C,  alpha,  I  )
  \mapsto \mathtt{InverseMorphismFromCoimageToImageWithGivenObjects}(C, alpha,
  I)[123X.[133X
  
  [1X7.6-91 AddIsAutomorphism[101X
  
  [33X[1;0Y[29X[2XAddIsAutomorphism[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given  function [23XF[123X to the category for the basic operation [10XIsAutomorphism[110X. [23XF:
  ( arg2 ) \mapsto \mathtt{IsAutomorphism}(arg2)[123X.[133X
  
  [1X7.6-92 AddIsBijectiveObject[101X
  
  [33X[1;0Y[29X[2XAddIsBijectiveObject[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given  function [23XF[123X to the category for the basic operation [10XIsBijectiveObject[110X.
  [23XF: ( arg2 ) \mapsto \mathtt{IsBijectiveObject}(arg2)[123X.[133X
  
  [1X7.6-93 AddIsCodominating[101X
  
  [33X[1;0Y[29X[2XAddIsCodominating[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given  function [23XF[123X to the category for the basic operation [10XIsCodominating[110X. [23XF:
  ( arg2, arg3 ) \mapsto \mathtt{IsCodominating}(arg2, arg3)[123X.[133X
  
  [1X7.6-94 AddIsColiftable[101X
  
  [33X[1;0Y[29X[2XAddIsColiftable[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given  function [23XF[123X to the category for the basic operation [10XIsColiftable[110X. [23XF: (
  arg2, arg3 ) \mapsto \mathtt{IsColiftable}(arg2, arg3)[123X.[133X
  
  [1X7.6-95 AddIsColiftableAlongEpimorphism[101X
  
  [33X[1;0Y[29X[2XAddIsColiftableAlongEpimorphism[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XIsColiftableAlongEpimorphism[110X.     [23XF:     (     arg2,    arg3    )    \mapsto
  \mathtt{IsColiftableAlongEpimorphism}(arg2, arg3)[123X.[133X
  
  [1X7.6-96 AddIsCongruentForMorphisms[101X
  
  [33X[1;0Y[29X[2XAddIsCongruentForMorphisms[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XIsCongruentForMorphisms[110X.      [23XF:      (     arg2,     arg3     )     \mapsto
  \mathtt{IsCongruentForMorphisms}(arg2, arg3)[123X.[133X
  
  [1X7.6-97 AddIsDominating[101X
  
  [33X[1;0Y[29X[2XAddIsDominating[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given  function [23XF[123X to the category for the basic operation [10XIsDominating[110X. [23XF: (
  arg2, arg3 ) \mapsto \mathtt{IsDominating}(arg2, arg3)[123X.[133X
  
  [1X7.6-98 AddIsEndomorphism[101X
  
  [33X[1;0Y[29X[2XAddIsEndomorphism[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given  function [23XF[123X to the category for the basic operation [10XIsEndomorphism[110X. [23XF:
  ( arg2 ) \mapsto \mathtt{IsEndomorphism}(arg2)[123X.[133X
  
  [1X7.6-99 AddIsEpimorphism[101X
  
  [33X[1;0Y[29X[2XAddIsEpimorphism[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given function [23XF[123X to the category for the basic operation [10XIsEpimorphism[110X. [23XF: (
  arg2 ) \mapsto \mathtt{IsEpimorphism}(arg2)[123X.[133X
  
  [1X7.6-100 AddIsEqualAsFactorobjects[101X
  
  [33X[1;0Y[29X[2XAddIsEqualAsFactorobjects[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XIsEqualAsFactorobjects[110X.      [23XF:      (      arg2,     arg3     )     \mapsto
  \mathtt{IsEqualAsFactorobjects}(arg2, arg3)[123X.[133X
  
  [1X7.6-101 AddIsEqualAsSubobjects[101X
  
  [33X[1;0Y[29X[2XAddIsEqualAsSubobjects[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XIsEqualAsSubobjects[110X.      [23XF:      (      arg2,      arg3      )      \mapsto
  \mathtt{IsEqualAsSubobjects}(arg2, arg3)[123X.[133X
  
  [1X7.6-102 AddIsEqualForCacheForMorphisms[101X
  
  [33X[1;0Y[29X[2XAddIsEqualForCacheForMorphisms[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XIsEqualForCacheForMorphisms[110X.     [23XF:     (     arg2,     arg3    )    \mapsto
  \mathtt{IsEqualForCacheForMorphisms}(arg2, arg3)[123X.[133X
  
  [1X7.6-103 AddIsEqualForCacheForObjects[101X
  
  [33X[1;0Y[29X[2XAddIsEqualForCacheForObjects[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XIsEqualForCacheForObjects[110X.     [23XF:     (     arg2,     arg3     )     \mapsto
  \mathtt{IsEqualForCacheForObjects}(arg2, arg3)[123X.[133X
  
  [1X7.6-104 AddIsEqualForMorphisms[101X
  
  [33X[1;0Y[29X[2XAddIsEqualForMorphisms[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XIsEqualForMorphisms[110X.      [23XF:      (      arg2,      arg3      )      \mapsto
  \mathtt{IsEqualForMorphisms}(arg2, arg3)[123X.[133X
  
  [1X7.6-105 AddIsEqualForMorphismsOnMor[101X
  
  [33X[1;0Y[29X[2XAddIsEqualForMorphismsOnMor[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XIsEqualForMorphismsOnMor[110X.      [23XF:     (     arg2,     arg3     )     \mapsto
  \mathtt{IsEqualForMorphismsOnMor}(arg2, arg3)[123X.[133X
  
  [1X7.6-106 AddIsEqualForObjects[101X
  
  [33X[1;0Y[29X[2XAddIsEqualForObjects[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given  function [23XF[123X to the category for the basic operation [10XIsEqualForObjects[110X.
  [23XF: ( arg2, arg3 ) \mapsto \mathtt{IsEqualForObjects}(arg2, arg3)[123X.[133X
  
  [1X7.6-107 AddIsEqualToIdentityMorphism[101X
  
  [33X[1;0Y[29X[2XAddIsEqualToIdentityMorphism[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XIsEqualToIdentityMorphism[110X.       [23XF:       (       arg2       )       \mapsto
  \mathtt{IsEqualToIdentityMorphism}(arg2)[123X.[133X
  
  [1X7.6-108 AddIsEqualToZeroMorphism[101X
  
  [33X[1;0Y[29X[2XAddIsEqualToZeroMorphism[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XIsEqualToZeroMorphism[110X.        [23XF:        (        arg2        )       \mapsto
  \mathtt{IsEqualToZeroMorphism}(arg2)[123X.[133X
  
  [1X7.6-109 AddIsHomSetInhabited[101X
  
  [33X[1;0Y[29X[2XAddIsHomSetInhabited[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given  function [23XF[123X to the category for the basic operation [10XIsHomSetInhabited[110X.
  [23XF: ( arg2, arg3 ) \mapsto \mathtt{IsHomSetInhabited}(arg2, arg3)[123X.[133X
  
  [1X7.6-110 AddIsIdempotent[101X
  
  [33X[1;0Y[29X[2XAddIsIdempotent[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given  function [23XF[123X to the category for the basic operation [10XIsIdempotent[110X. [23XF: (
  arg2 ) \mapsto \mathtt{IsIdempotent}(arg2)[123X.[133X
  
  [1X7.6-111 AddIsInitial[101X
  
  [33X[1;0Y[29X[2XAddIsInitial[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given  function  [23XF[123X  to  the category for the basic operation [10XIsInitial[110X. [23XF: (
  arg2 ) \mapsto \mathtt{IsInitial}(arg2)[123X.[133X
  
  [1X7.6-112 AddIsInjective[101X
  
  [33X[1;0Y[29X[2XAddIsInjective[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given  function  [23XF[123X to the category for the basic operation [10XIsInjective[110X. [23XF: (
  arg2 ) \mapsto \mathtt{IsInjective}(arg2)[123X.[133X
  
  [1X7.6-113 AddIsIsomorphism[101X
  
  [33X[1;0Y[29X[2XAddIsIsomorphism[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given function [23XF[123X to the category for the basic operation [10XIsIsomorphism[110X. [23XF: (
  arg2 ) \mapsto \mathtt{IsIsomorphism}(arg2)[123X.[133X
  
  [1X7.6-114 AddIsLiftable[101X
  
  [33X[1;0Y[29X[2XAddIsLiftable[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given  function  [23XF[123X  to the category for the basic operation [10XIsLiftable[110X. [23XF: (
  arg2, arg3 ) \mapsto \mathtt{IsLiftable}(arg2, arg3)[123X.[133X
  
  [1X7.6-115 AddIsLiftableAlongMonomorphism[101X
  
  [33X[1;0Y[29X[2XAddIsLiftableAlongMonomorphism[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XIsLiftableAlongMonomorphism[110X.     [23XF:     (     arg2,     arg3    )    \mapsto
  \mathtt{IsLiftableAlongMonomorphism}(arg2, arg3)[123X.[133X
  
  [1X7.6-116 AddIsMonomorphism[101X
  
  [33X[1;0Y[29X[2XAddIsMonomorphism[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given  function [23XF[123X to the category for the basic operation [10XIsMonomorphism[110X. [23XF:
  ( arg2 ) \mapsto \mathtt{IsMonomorphism}(arg2)[123X.[133X
  
  [1X7.6-117 AddIsOne[101X
  
  [33X[1;0Y[29X[2XAddIsOne[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given  function [23XF[123X to the category for the basic operation [10XIsOne[110X. [23XF: ( arg2 )
  \mapsto \mathtt{IsOne}(arg2)[123X.[133X
  
  [1X7.6-118 AddIsProjective[101X
  
  [33X[1;0Y[29X[2XAddIsProjective[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given  function [23XF[123X to the category for the basic operation [10XIsProjective[110X. [23XF: (
  arg2 ) \mapsto \mathtt{IsProjective}(arg2)[123X.[133X
  
  [1X7.6-119 AddIsSplitEpimorphism[101X
  
  [33X[1;0Y[29X[2XAddIsSplitEpimorphism[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given function [23XF[123X to the category for the basic operation [10XIsSplitEpimorphism[110X.
  [23XF: ( arg2 ) \mapsto \mathtt{IsSplitEpimorphism}(arg2)[123X.[133X
  
  [1X7.6-120 AddIsSplitMonomorphism[101X
  
  [33X[1;0Y[29X[2XAddIsSplitMonomorphism[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XIsSplitMonomorphism[110X. [23XF: ( arg2 ) \mapsto \mathtt{IsSplitMonomorphism}(arg2)[123X.[133X
  
  [1X7.6-121 AddIsTerminal[101X
  
  [33X[1;0Y[29X[2XAddIsTerminal[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given  function  [23XF[123X  to the category for the basic operation [10XIsTerminal[110X. [23XF: (
  arg2 ) \mapsto \mathtt{IsTerminal}(arg2)[123X.[133X
  
  [1X7.6-122 AddIsWellDefinedForMorphisms[101X
  
  [33X[1;0Y[29X[2XAddIsWellDefinedForMorphisms[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XIsWellDefinedForMorphisms[110X.       [23XF:       (       arg2       )       \mapsto
  \mathtt{IsWellDefinedForMorphisms}(arg2)[123X.[133X
  
  [1X7.6-123 AddIsWellDefinedForObjects[101X
  
  [33X[1;0Y[29X[2XAddIsWellDefinedForObjects[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XIsWellDefinedForObjects[110X.        [23XF:        (       arg2       )       \mapsto
  \mathtt{IsWellDefinedForObjects}(arg2)[123X.[133X
  
  [1X7.6-124 AddIsWellDefinedForTwoCells[101X
  
  [33X[1;0Y[29X[2XAddIsWellDefinedForTwoCells[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XIsWellDefinedForTwoCells[110X.        [23XF:       (       arg2       )       \mapsto
  \mathtt{IsWellDefinedForTwoCells}(arg2)[123X.[133X
  
  [1X7.6-125 AddIsZeroForMorphisms[101X
  
  [33X[1;0Y[29X[2XAddIsZeroForMorphisms[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given function [23XF[123X to the category for the basic operation [10XIsZeroForMorphisms[110X.
  [23XF: ( arg2 ) \mapsto \mathtt{IsZeroForMorphisms}(arg2)[123X.[133X
  
  [1X7.6-126 AddIsZeroForObjects[101X
  
  [33X[1;0Y[29X[2XAddIsZeroForObjects[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given  function  [23XF[123X to the category for the basic operation [10XIsZeroForObjects[110X.
  [23XF: ( arg2 ) \mapsto \mathtt{IsZeroForObjects}(arg2)[123X.[133X
  
  [1X7.6-127 AddIsomorphismFromCoequalizerOfCoproductDiagramToPushout[101X
  
  [33X[1;0Y[29X[2XAddIsomorphismFromCoequalizerOfCoproductDiagramToPushout[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XIsomorphismFromCoequalizerOfCoproductDiagramToPushout[110X.  [23XF:  (  D  )  \mapsto
  \mathtt{IsomorphismFromCoequalizerOfCoproductDiagramToPushout}(D)[123X.[133X
  
  [1X7.6-128 AddIsomorphismFromCoimageToCokernelOfKernel[101X
  
  [33X[1;0Y[29X[2XAddIsomorphismFromCoimageToCokernelOfKernel[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XIsomorphismFromCoimageToCokernelOfKernel[110X.    [23XF:    (    alpha    )   \mapsto
  \mathtt{IsomorphismFromCoimageToCokernelOfKernel}(alpha)[123X.[133X
  
  [1X7.6-129 AddIsomorphismFromCokernelOfDiagonalDifferenceToPushout[101X
  
  [33X[1;0Y[29X[2XAddIsomorphismFromCokernelOfDiagonalDifferenceToPushout[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XIsomorphismFromCokernelOfDiagonalDifferenceToPushout[110X.   [23XF:  (  D  )  \mapsto
  \mathtt{IsomorphismFromCokernelOfDiagonalDifferenceToPushout}(D)[123X.[133X
  
  [1X7.6-130 AddIsomorphismFromCokernelOfKernelToCoimage[101X
  
  [33X[1;0Y[29X[2XAddIsomorphismFromCokernelOfKernelToCoimage[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XIsomorphismFromCokernelOfKernelToCoimage[110X.    [23XF:    (    alpha    )   \mapsto
  \mathtt{IsomorphismFromCokernelOfKernelToCoimage}(alpha)[123X.[133X
  
  [1X7.6-131 AddIsomorphismFromCoproductToDirectSum[101X
  
  [33X[1;0Y[29X[2XAddIsomorphismFromCoproductToDirectSum[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XIsomorphismFromCoproductToDirectSum[110X.      [23XF:      (      D     )     \mapsto
  \mathtt{IsomorphismFromCoproductToDirectSum}(D)[123X.[133X
  
  [1X7.6-132 AddIsomorphismFromDirectProductToDirectSum[101X
  
  [33X[1;0Y[29X[2XAddIsomorphismFromDirectProductToDirectSum[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XIsomorphismFromDirectProductToDirectSum[110X.     [23XF:     (     D     )    \mapsto
  \mathtt{IsomorphismFromDirectProductToDirectSum}(D)[123X.[133X
  
  [1X7.6-133 AddIsomorphismFromDirectSumToCoproduct[101X
  
  [33X[1;0Y[29X[2XAddIsomorphismFromDirectSumToCoproduct[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XIsomorphismFromDirectSumToCoproduct[110X.      [23XF:      (      D     )     \mapsto
  \mathtt{IsomorphismFromDirectSumToCoproduct}(D)[123X.[133X
  
  [1X7.6-134 AddIsomorphismFromDirectSumToDirectProduct[101X
  
  [33X[1;0Y[29X[2XAddIsomorphismFromDirectSumToDirectProduct[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XIsomorphismFromDirectSumToDirectProduct[110X.     [23XF:     (     D     )    \mapsto
  \mathtt{IsomorphismFromDirectSumToDirectProduct}(D)[123X.[133X
  
  [1X7.6-135 AddIsomorphismFromEqualizerOfDirectProductDiagramToFiberProduct[101X
  
  [33X[1;0Y[29X[2XAddIsomorphismFromEqualizerOfDirectProductDiagramToFiberProduct[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XIsomorphismFromEqualizerOfDirectProductDiagramToFiberProduct[110X.   [23XF:   (  D  )
  \mapsto
  \mathtt{IsomorphismFromEqualizerOfDirectProductDiagramToFiberProduct}(D)[123X.[133X
  
  [1X7.6-136 AddIsomorphismFromFiberProductToEqualizerOfDirectProductDiagram[101X
  
  [33X[1;0Y[29X[2XAddIsomorphismFromFiberProductToEqualizerOfDirectProductDiagram[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XIsomorphismFromFiberProductToEqualizerOfDirectProductDiagram[110X.   [23XF:   (  D  )
  \mapsto
  \mathtt{IsomorphismFromFiberProductToEqualizerOfDirectProductDiagram}(D)[123X.[133X
  
  [1X7.6-137 AddIsomorphismFromFiberProductToKernelOfDiagonalDifference[101X
  
  [33X[1;0Y[29X[2XAddIsomorphismFromFiberProductToKernelOfDiagonalDifference[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XIsomorphismFromFiberProductToKernelOfDiagonalDifference[110X.  [23XF:  (  D ) \mapsto
  \mathtt{IsomorphismFromFiberProductToKernelOfDiagonalDifference}(D)[123X.[133X
  
  [1X7.6-138 AddIsomorphismFromHomologyObjectToItsConstructionAsAnImageObject[101X
  
  [33X[1;0Y[29X[2XAddIsomorphismFromHomologyObjectToItsConstructionAsAnImageObject[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XIsomorphismFromHomologyObjectToItsConstructionAsAnImageObject[110X.  [23XF:  ( alpha,
  beta                                )                                \mapsto
  \mathtt{IsomorphismFromHomologyObjectToItsConstructionAsAnImageObject}(alpha,
  beta)[123X.[133X
  
  [1X7.6-139 AddIsomorphismFromImageObjectToKernelOfCokernel[101X
  
  [33X[1;0Y[29X[2XAddIsomorphismFromImageObjectToKernelOfCokernel[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XIsomorphismFromImageObjectToKernelOfCokernel[110X.   [23XF:   (   alpha   )   \mapsto
  \mathtt{IsomorphismFromImageObjectToKernelOfCokernel}(alpha)[123X.[133X
  
  [1X7.6-140 AddIsomorphismFromInitialObjectToZeroObject[101X
  
  [33X[1;0Y[29X[2XAddIsomorphismFromInitialObjectToZeroObject[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XIsomorphismFromInitialObjectToZeroObject[110X.      [23XF:      (      )      \mapsto
  \mathtt{IsomorphismFromInitialObjectToZeroObject}()[123X.[133X
  
  [1X7.6-141 AddIsomorphismFromItsConstructionAsAnImageObjectToHomologyObject[101X
  
  [33X[1;0Y[29X[2XAddIsomorphismFromItsConstructionAsAnImageObjectToHomologyObject[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XIsomorphismFromItsConstructionAsAnImageObjectToHomologyObject[110X.  [23XF:  ( alpha,
  beta                                )                                \mapsto
  \mathtt{IsomorphismFromItsConstructionAsAnImageObjectToHomologyObject}(alpha,
  beta)[123X.[133X
  
  [1X7.6-142 AddIsomorphismFromKernelOfCokernelToImageObject[101X
  
  [33X[1;0Y[29X[2XAddIsomorphismFromKernelOfCokernelToImageObject[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XIsomorphismFromKernelOfCokernelToImageObject[110X.   [23XF:   (   alpha   )   \mapsto
  \mathtt{IsomorphismFromKernelOfCokernelToImageObject}(alpha)[123X.[133X
  
  [1X7.6-143 AddIsomorphismFromKernelOfDiagonalDifferenceToFiberProduct[101X
  
  [33X[1;0Y[29X[2XAddIsomorphismFromKernelOfDiagonalDifferenceToFiberProduct[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XIsomorphismFromKernelOfDiagonalDifferenceToFiberProduct[110X.  [23XF:  (  D ) \mapsto
  \mathtt{IsomorphismFromKernelOfDiagonalDifferenceToFiberProduct}(D)[123X.[133X
  
  [1X7.6-144 AddIsomorphismFromPushoutToCoequalizerOfCoproductDiagram[101X
  
  [33X[1;0Y[29X[2XAddIsomorphismFromPushoutToCoequalizerOfCoproductDiagram[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XIsomorphismFromPushoutToCoequalizerOfCoproductDiagram[110X.  [23XF:  (  D  )  \mapsto
  \mathtt{IsomorphismFromPushoutToCoequalizerOfCoproductDiagram}(D)[123X.[133X
  
  [1X7.6-145 AddIsomorphismFromPushoutToCokernelOfDiagonalDifference[101X
  
  [33X[1;0Y[29X[2XAddIsomorphismFromPushoutToCokernelOfDiagonalDifference[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XIsomorphismFromPushoutToCokernelOfDiagonalDifference[110X.   [23XF:  (  D  )  \mapsto
  \mathtt{IsomorphismFromPushoutToCokernelOfDiagonalDifference}(D)[123X.[133X
  
  [1X7.6-146 AddIsomorphismFromTerminalObjectToZeroObject[101X
  
  [33X[1;0Y[29X[2XAddIsomorphismFromTerminalObjectToZeroObject[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XIsomorphismFromTerminalObjectToZeroObject[110X.      [23XF:      (      )     \mapsto
  \mathtt{IsomorphismFromTerminalObjectToZeroObject}()[123X.[133X
  
  [1X7.6-147 AddIsomorphismFromZeroObjectToInitialObject[101X
  
  [33X[1;0Y[29X[2XAddIsomorphismFromZeroObjectToInitialObject[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XIsomorphismFromZeroObjectToInitialObject[110X.      [23XF:      (      )      \mapsto
  \mathtt{IsomorphismFromZeroObjectToInitialObject}()[123X.[133X
  
  [1X7.6-148 AddIsomorphismFromZeroObjectToTerminalObject[101X
  
  [33X[1;0Y[29X[2XAddIsomorphismFromZeroObjectToTerminalObject[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XIsomorphismFromZeroObjectToTerminalObject[110X.      [23XF:      (      )     \mapsto
  \mathtt{IsomorphismFromZeroObjectToTerminalObject}()[123X.[133X
  
  [1X7.6-149 AddKernelEmbedding[101X
  
  [33X[1;0Y[29X[2XAddKernelEmbedding[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given function [23XF[123X to the category for the basic operation [10XKernelEmbedding[110X. [23XF:
  ( alpha ) \mapsto \mathtt{KernelEmbedding}(alpha)[123X.[133X
  
  [1X7.6-150 AddKernelEmbeddingWithGivenKernelObject[101X
  
  [33X[1;0Y[29X[2XAddKernelEmbeddingWithGivenKernelObject[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XKernelEmbeddingWithGivenKernelObject[110X.    [23XF:    (    alpha,   P   )   \mapsto
  \mathtt{KernelEmbeddingWithGivenKernelObject}(alpha, P)[123X.[133X
  
  [1X7.6-151 AddKernelLift[101X
  
  [33X[1;0Y[29X[2XAddKernelLift[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given  function  [23XF[123X  to the category for the basic operation [10XKernelLift[110X. [23XF: (
  alpha, T, tau ) \mapsto \mathtt{KernelLift}(alpha, T, tau)[123X.[133X
  
  [1X7.6-152 AddKernelLiftWithGivenKernelObject[101X
  
  [33X[1;0Y[29X[2XAddKernelLiftWithGivenKernelObject[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XKernelLiftWithGivenKernelObject[110X.   [23XF:   (   alpha,   T,  tau,  P  )  \mapsto
  \mathtt{KernelLiftWithGivenKernelObject}(alpha, T, tau, P)[123X.[133X
  
  [1X7.6-153 AddKernelObject[101X
  
  [33X[1;0Y[29X[2XAddKernelObject[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given  function [23XF[123X to the category for the basic operation [10XKernelObject[110X. [23XF: (
  arg2 ) \mapsto \mathtt{KernelObject}(arg2)[123X.[133X
  
  [1X7.6-154 AddKernelObjectFunctorial[101X
  
  [33X[1;0Y[29X[2XAddKernelObjectFunctorial[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XKernelObjectFunctorial[110X.    [23XF:    (    alpha,    mu,    alphap    )   \mapsto
  \mathtt{KernelObjectFunctorial}(alpha, mu, alphap)[123X.[133X
  
  [1X7.6-155 AddKernelObjectFunctorialWithGivenKernelObjects[101X
  
  [33X[1;0Y[29X[2XAddKernelObjectFunctorialWithGivenKernelObjects[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XKernelObjectFunctorialWithGivenKernelObjects[110X.  [23XF: ( P, alpha, mu, alphap, Pp
  )  \mapsto  \mathtt{KernelObjectFunctorialWithGivenKernelObjects}(P,  alpha,
  mu, alphap, Pp)[123X.[133X
  
  [1X7.6-156 AddLift[101X
  
  [33X[1;0Y[29X[2XAddLift[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given  function  [23XF[123X to the category for the basic operation [10XLift[110X. [23XF: ( alpha,
  beta ) \mapsto \mathtt{Lift}(alpha, beta)[123X.[133X
  
  [1X7.6-157 AddLiftAlongMonomorphism[101X
  
  [33X[1;0Y[29X[2XAddLiftAlongMonomorphism[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XLiftAlongMonomorphism[110X.      [23XF:      (      iota,      tau      )     \mapsto
  \mathtt{LiftAlongMonomorphism}(iota, tau)[123X.[133X
  
  [1X7.6-158 AddLiftOrFail[101X
  
  [33X[1;0Y[29X[2XAddLiftOrFail[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given  function  [23XF[123X  to the category for the basic operation [10XLiftOrFail[110X. [23XF: (
  alpha, beta ) \mapsto \mathtt{LiftOrFail}(alpha, beta)[123X.[133X
  
  [1X7.6-159 AddMereExistenceOfSolutionOfLinearSystemInAbCategory[101X
  
  [33X[1;0Y[29X[2XAddMereExistenceOfSolutionOfLinearSystemInAbCategory[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XMereExistenceOfSolutionOfLinearSystemInAbCategory[110X.  [23XF:  ( arg2, arg3, arg4 )
  \mapsto     \mathtt{MereExistenceOfSolutionOfLinearSystemInAbCategory}(arg2,
  arg3, arg4)[123X.[133X
  
  [1X7.6-160 AddMonomorphismIntoInjectiveEnvelopeObject[101X
  
  [33X[1;0Y[29X[2XAddMonomorphismIntoInjectiveEnvelopeObject[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XMonomorphismIntoInjectiveEnvelopeObject[110X.     [23XF:     (     A     )    \mapsto
  \mathtt{MonomorphismIntoInjectiveEnvelopeObject}(A)[123X.[133X
  
  [1X7.6-161 AddMonomorphismIntoInjectiveEnvelopeObjectWithGivenInjectiveEnvelopeObject[101X
  
  [33X[1;0Y[29X[2XAddMonomorphismIntoInjectiveEnvelopeObjectWithGivenInjectiveEnvelopeObject[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XMonomorphismIntoInjectiveEnvelopeObjectWithGivenInjectiveEnvelopeObject[110X.  [23XF:
  (                A,                I                )                \mapsto
  \mathtt{MonomorphismIntoInjectiveEnvelopeObjectWithGivenInjectiveEnvelopeObject}(A,
  I)[123X.[133X
  
  [1X7.6-162 AddMonomorphismIntoSomeInjectiveObject[101X
  
  [33X[1;0Y[29X[2XAddMonomorphismIntoSomeInjectiveObject[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XMonomorphismIntoSomeInjectiveObject[110X.      [23XF:      (      A     )     \mapsto
  \mathtt{MonomorphismIntoSomeInjectiveObject}(A)[123X.[133X
  
  [1X7.6-163 AddMonomorphismIntoSomeInjectiveObjectWithGivenSomeInjectiveObject[101X
  
  [33X[1;0Y[29X[2XAddMonomorphismIntoSomeInjectiveObjectWithGivenSomeInjectiveObject[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XMonomorphismIntoSomeInjectiveObjectWithGivenSomeInjectiveObject[110X. [23XF: ( A, I )
  \mapsto
  \mathtt{MonomorphismIntoSomeInjectiveObjectWithGivenSomeInjectiveObject}(A,
  I)[123X.[133X
  
  [1X7.6-164 AddMorphismBetweenDirectSums[101X
  
  [33X[1;0Y[29X[2XAddMorphismBetweenDirectSums[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XMorphismBetweenDirectSums[110X. [23XF: ( source_diagram, mat, range_diagram ) \mapsto
  \mathtt{MorphismBetweenDirectSums}(source_diagram, mat, range_diagram)[123X.[133X
  
  [1X7.6-165 AddMorphismBetweenDirectSumsWithGivenDirectSums[101X
  
  [33X[1;0Y[29X[2XAddMorphismBetweenDirectSumsWithGivenDirectSums[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XMorphismBetweenDirectSumsWithGivenDirectSums[110X.  [23XF:  ( S, source_diagram, mat,
  range_diagram,                  T                  )                 \mapsto
  \mathtt{MorphismBetweenDirectSumsWithGivenDirectSums}(S,     source_diagram,
  mat, range_diagram, T)[123X.[133X
  
  [1X7.6-166 AddMorphismConstructor[101X
  
  [33X[1;0Y[29X[2XAddMorphismConstructor[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XMorphismConstructor[110X.     [23XF:     (     arg2,    arg3,    arg4    )    \mapsto
  \mathtt{MorphismConstructor}(arg2, arg3, arg4)[123X.[133X
  
  [1X7.6-167 AddMorphismDatum[101X
  
  [33X[1;0Y[29X[2XAddMorphismDatum[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given function [23XF[123X to the category for the basic operation [10XMorphismDatum[110X. [23XF: (
  arg2 ) \mapsto \mathtt{MorphismDatum}(arg2)[123X.[133X
  
  [1X7.6-168 AddMorphismFromCoimageToImageWithGivenObjects[101X
  
  [33X[1;0Y[29X[2XAddMorphismFromCoimageToImageWithGivenObjects[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XMorphismFromCoimageToImageWithGivenObjects[110X.  [23XF:  (  C,  alpha,  I  ) \mapsto
  \mathtt{MorphismFromCoimageToImageWithGivenObjects}(C, alpha, I)[123X.[133X
  
  [1X7.6-169 AddMorphismFromEqualizerToSink[101X
  
  [33X[1;0Y[29X[2XAddMorphismFromEqualizerToSink[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XMorphismFromEqualizerToSink[110X.     [23XF:     (    Y,    morphisms    )    \mapsto
  \mathtt{MorphismFromEqualizerToSink}(Y, morphisms)[123X.[133X
  
  [1X7.6-170 AddMorphismFromEqualizerToSinkWithGivenEqualizer[101X
  
  [33X[1;0Y[29X[2XAddMorphismFromEqualizerToSinkWithGivenEqualizer[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XMorphismFromEqualizerToSinkWithGivenEqualizer[110X.   [23XF:  (  Y,  morphisms,  P  )
  \mapsto \mathtt{MorphismFromEqualizerToSinkWithGivenEqualizer}(Y, morphisms,
  P)[123X.[133X
  
  [1X7.6-171 AddMorphismFromFiberProductToSink[101X
  
  [33X[1;0Y[29X[2XAddMorphismFromFiberProductToSink[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XMorphismFromFiberProductToSink[110X.     [23XF:     (     morphisms     )     \mapsto
  \mathtt{MorphismFromFiberProductToSink}(morphisms)[123X.[133X
  
  [1X7.6-172 AddMorphismFromFiberProductToSinkWithGivenFiberProduct[101X
  
  [33X[1;0Y[29X[2XAddMorphismFromFiberProductToSinkWithGivenFiberProduct[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XMorphismFromFiberProductToSinkWithGivenFiberProduct[110X.  [23XF:  (  morphisms,  P )
  \mapsto
  \mathtt{MorphismFromFiberProductToSinkWithGivenFiberProduct}(morphisms, P)[123X.[133X
  
  [1X7.6-173 AddMorphismFromKernelObjectToSink[101X
  
  [33X[1;0Y[29X[2XAddMorphismFromKernelObjectToSink[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XMorphismFromKernelObjectToSink[110X.      [23XF:      (      alpha      )     \mapsto
  \mathtt{MorphismFromKernelObjectToSink}(alpha)[123X.[133X
  
  [1X7.6-174 AddMorphismFromKernelObjectToSinkWithGivenKernelObject[101X
  
  [33X[1;0Y[29X[2XAddMorphismFromKernelObjectToSinkWithGivenKernelObject[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XMorphismFromKernelObjectToSinkWithGivenKernelObject[110X. [23XF: ( alpha, P ) \mapsto
  \mathtt{MorphismFromKernelObjectToSinkWithGivenKernelObject}(alpha, P)[123X.[133X
  
  [1X7.6-175 AddMorphismFromSourceToCoequalizer[101X
  
  [33X[1;0Y[29X[2XAddMorphismFromSourceToCoequalizer[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XMorphismFromSourceToCoequalizer[110X.    [23XF:    (    Y,    morphisms   )   \mapsto
  \mathtt{MorphismFromSourceToCoequalizer}(Y, morphisms)[123X.[133X
  
  [1X7.6-176 AddMorphismFromSourceToCoequalizerWithGivenCoequalizer[101X
  
  [33X[1;0Y[29X[2XAddMorphismFromSourceToCoequalizerWithGivenCoequalizer[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XMorphismFromSourceToCoequalizerWithGivenCoequalizer[110X.  [23XF: ( Y, morphisms, P )
  \mapsto      \mathtt{MorphismFromSourceToCoequalizerWithGivenCoequalizer}(Y,
  morphisms, P)[123X.[133X
  
  [1X7.6-177 AddMorphismFromSourceToCokernelObject[101X
  
  [33X[1;0Y[29X[2XAddMorphismFromSourceToCokernelObject[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XMorphismFromSourceToCokernelObject[110X.     [23XF:     (     alpha     )     \mapsto
  \mathtt{MorphismFromSourceToCokernelObject}(alpha)[123X.[133X
  
  [1X7.6-178 AddMorphismFromSourceToCokernelObjectWithGivenCokernelObject[101X
  
  [33X[1;0Y[29X[2XAddMorphismFromSourceToCokernelObjectWithGivenCokernelObject[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XMorphismFromSourceToCokernelObjectWithGivenCokernelObject[110X.  [23XF:  ( alpha, P )
  \mapsto
  \mathtt{MorphismFromSourceToCokernelObjectWithGivenCokernelObject}(alpha,
  P)[123X.[133X
  
  [1X7.6-179 AddMorphismFromSourceToPushout[101X
  
  [33X[1;0Y[29X[2XAddMorphismFromSourceToPushout[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XMorphismFromSourceToPushout[110X.      [23XF:      (      morphisms     )     \mapsto
  \mathtt{MorphismFromSourceToPushout}(morphisms)[123X.[133X
  
  [1X7.6-180 AddMorphismFromSourceToPushoutWithGivenPushout[101X
  
  [33X[1;0Y[29X[2XAddMorphismFromSourceToPushoutWithGivenPushout[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XMorphismFromSourceToPushoutWithGivenPushout[110X.  [23XF:  (  morphisms,  P ) \mapsto
  \mathtt{MorphismFromSourceToPushoutWithGivenPushout}(morphisms, P)[123X.[133X
  
  [1X7.6-181 AddMultiplyWithElementOfCommutativeRingForMorphisms[101X
  
  [33X[1;0Y[29X[2XAddMultiplyWithElementOfCommutativeRingForMorphisms[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XMultiplyWithElementOfCommutativeRingForMorphisms[110X.   [23XF:  (  r,  a  )  \mapsto
  \mathtt{MultiplyWithElementOfCommutativeRingForMorphisms}(r, a)[123X.[133X
  
  [1X7.6-182 AddObjectConstructor[101X
  
  [33X[1;0Y[29X[2XAddObjectConstructor[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given  function [23XF[123X to the category for the basic operation [10XObjectConstructor[110X.
  [23XF: ( arg2 ) \mapsto \mathtt{ObjectConstructor}(arg2)[123X.[133X
  
  [1X7.6-183 AddObjectDatum[101X
  
  [33X[1;0Y[29X[2XAddObjectDatum[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given  function  [23XF[123X to the category for the basic operation [10XObjectDatum[110X. [23XF: (
  arg2 ) \mapsto \mathtt{ObjectDatum}(arg2)[123X.[133X
  
  [1X7.6-184 AddPostCompose[101X
  
  [33X[1;0Y[29X[2XAddPostCompose[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given  function  [23XF[123X to the category for the basic operation [10XPostCompose[110X. [23XF: (
  beta, alpha ) \mapsto \mathtt{PostCompose}(beta, alpha)[123X.[133X
  
  [1X7.6-185 AddPostComposeList[101X
  
  [33X[1;0Y[29X[2XAddPostComposeList[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given function [23XF[123X to the category for the basic operation [10XPostComposeList[110X. [23XF:
  ( list_of_morphisms ) \mapsto \mathtt{PostComposeList}(list_of_morphisms)[123X.[133X
  
  [1X7.6-186 AddPostInverseForMorphisms[101X
  
  [33X[1;0Y[29X[2XAddPostInverseForMorphisms[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XPostInverseForMorphisms[110X.        [23XF:       (       alpha       )       \mapsto
  \mathtt{PostInverseForMorphisms}(alpha)[123X.[133X
  
  [1X7.6-187 AddPreCompose[101X
  
  [33X[1;0Y[29X[2XAddPreCompose[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given  function  [23XF[123X  to the category for the basic operation [10XPreCompose[110X. [23XF: (
  alpha, beta ) \mapsto \mathtt{PreCompose}(alpha, beta)[123X.[133X
  
  [1X7.6-188 AddPreComposeList[101X
  
  [33X[1;0Y[29X[2XAddPreComposeList[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given  function [23XF[123X to the category for the basic operation [10XPreComposeList[110X. [23XF:
  ( list_of_morphisms ) \mapsto \mathtt{PreComposeList}(list_of_morphisms)[123X.[133X
  
  [1X7.6-189 AddPreInverseForMorphisms[101X
  
  [33X[1;0Y[29X[2XAddPreInverseForMorphisms[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XPreInverseForMorphisms[110X.        [23XF:        (       alpha       )       \mapsto
  \mathtt{PreInverseForMorphisms}(alpha)[123X.[133X
  
  [1X7.6-190 AddProjectionInFactorOfDirectProduct[101X
  
  [33X[1;0Y[29X[2XAddProjectionInFactorOfDirectProduct[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XProjectionInFactorOfDirectProduct[110X.    [23XF:    (    objects,    k   )   \mapsto
  \mathtt{ProjectionInFactorOfDirectProduct}(objects, k)[123X.[133X
  
  [1X7.6-191 AddProjectionInFactorOfDirectProductWithGivenDirectProduct[101X
  
  [33X[1;0Y[29X[2XAddProjectionInFactorOfDirectProductWithGivenDirectProduct[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XProjectionInFactorOfDirectProductWithGivenDirectProduct[110X.  [23XF: ( objects, k, P
  )                                                                    \mapsto
  \mathtt{ProjectionInFactorOfDirectProductWithGivenDirectProduct}(objects, k,
  P)[123X.[133X
  
  [1X7.6-192 AddProjectionInFactorOfDirectSum[101X
  
  [33X[1;0Y[29X[2XAddProjectionInFactorOfDirectSum[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XProjectionInFactorOfDirectSum[110X.     [23XF:     (    objects,    k    )    \mapsto
  \mathtt{ProjectionInFactorOfDirectSum}(objects, k)[123X.[133X
  
  [1X7.6-193 AddProjectionInFactorOfDirectSumWithGivenDirectSum[101X
  
  [33X[1;0Y[29X[2XAddProjectionInFactorOfDirectSumWithGivenDirectSum[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XProjectionInFactorOfDirectSumWithGivenDirectSum[110X.   [23XF:  (  objects,  k,  P  )
  \mapsto \mathtt{ProjectionInFactorOfDirectSumWithGivenDirectSum}(objects, k,
  P)[123X.[133X
  
  [1X7.6-194 AddProjectionInFactorOfFiberProduct[101X
  
  [33X[1;0Y[29X[2XAddProjectionInFactorOfFiberProduct[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XProjectionInFactorOfFiberProduct[110X.    [23XF:    (    morphisms,   k   )   \mapsto
  \mathtt{ProjectionInFactorOfFiberProduct}(morphisms, k)[123X.[133X
  
  [1X7.6-195 AddProjectionInFactorOfFiberProductWithGivenFiberProduct[101X
  
  [33X[1;0Y[29X[2XAddProjectionInFactorOfFiberProductWithGivenFiberProduct[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XProjectionInFactorOfFiberProductWithGivenFiberProduct[110X.  [23XF: ( morphisms, k, P
  )                                                                    \mapsto
  \mathtt{ProjectionInFactorOfFiberProductWithGivenFiberProduct}(morphisms, k,
  P)[123X.[133X
  
  [1X7.6-196 AddProjectionOntoCoequalizer[101X
  
  [33X[1;0Y[29X[2XAddProjectionOntoCoequalizer[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XProjectionOntoCoequalizer[110X.     [23XF:     (     Y,     morphisms    )    \mapsto
  \mathtt{ProjectionOntoCoequalizer}(Y, morphisms)[123X.[133X
  
  [1X7.6-197 AddProjectionOntoCoequalizerWithGivenCoequalizer[101X
  
  [33X[1;0Y[29X[2XAddProjectionOntoCoequalizerWithGivenCoequalizer[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XProjectionOntoCoequalizerWithGivenCoequalizer[110X.   [23XF:  (  Y,  morphisms,  P  )
  \mapsto \mathtt{ProjectionOntoCoequalizerWithGivenCoequalizer}(Y, morphisms,
  P)[123X.[133X
  
  [1X7.6-198 AddProjectiveCoverObject[101X
  
  [33X[1;0Y[29X[2XAddProjectiveCoverObject[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XProjectiveCoverObject[110X.        [23XF:        (        arg2        )       \mapsto
  \mathtt{ProjectiveCoverObject}(arg2)[123X.[133X
  
  [1X7.6-199 AddProjectiveDimension[101X
  
  [33X[1;0Y[29X[2XAddProjectiveDimension[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XProjectiveDimension[110X. [23XF: ( arg2 ) \mapsto \mathtt{ProjectiveDimension}(arg2)[123X.[133X
  
  [1X7.6-200 AddProjectiveLift[101X
  
  [33X[1;0Y[29X[2XAddProjectiveLift[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given  function [23XF[123X to the category for the basic operation [10XProjectiveLift[110X. [23XF:
  ( alpha, beta ) \mapsto \mathtt{ProjectiveLift}(alpha, beta)[123X.[133X
  
  [1X7.6-201 AddPushout[101X
  
  [33X[1;0Y[29X[2XAddPushout[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given  function [23XF[123X to the category for the basic operation [10XPushout[110X. [23XF: ( arg2
  ) \mapsto \mathtt{Pushout}(arg2)[123X.[133X
  
  [1X7.6-202 AddPushoutFunctorial[101X
  
  [33X[1;0Y[29X[2XAddPushoutFunctorial[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given  function [23XF[123X to the category for the basic operation [10XPushoutFunctorial[110X.
  [23XF:        (       morphisms,       L,       morphismsp       )       \mapsto
  \mathtt{PushoutFunctorial}(morphisms, L, morphismsp)[123X.[133X
  
  [1X7.6-203 AddPushoutFunctorialWithGivenPushouts[101X
  
  [33X[1;0Y[29X[2XAddPushoutFunctorialWithGivenPushouts[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XPushoutFunctorialWithGivenPushouts[110X.  [23XF:  ( P, morphisms, L, morphismsp, Pp )
  \mapsto    \mathtt{PushoutFunctorialWithGivenPushouts}(P,    morphisms,   L,
  morphismsp, Pp)[123X.[133X
  
  [1X7.6-204 AddRandomMorphismByInteger[101X
  
  [33X[1;0Y[29X[2XAddRandomMorphismByInteger[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XRandomMorphismByInteger[110X.        [23XF:        (        n        )        \mapsto
  \mathtt{RandomMorphismByInteger}(n)[123X.[133X
  
  [1X7.6-205 AddRandomMorphismByList[101X
  
  [33X[1;0Y[29X[2XAddRandomMorphismByList[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XRandomMorphismByList[110X. [23XF: ( L ) \mapsto \mathtt{RandomMorphismByList}(L)[123X.[133X
  
  [1X7.6-206 AddRandomMorphismWithFixedRangeByInteger[101X
  
  [33X[1;0Y[29X[2XAddRandomMorphismWithFixedRangeByInteger[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XRandomMorphismWithFixedRangeByInteger[110X.    [23XF:    (    B,    n    )    \mapsto
  \mathtt{RandomMorphismWithFixedRangeByInteger}(B, n)[123X.[133X
  
  [1X7.6-207 AddRandomMorphismWithFixedRangeByList[101X
  
  [33X[1;0Y[29X[2XAddRandomMorphismWithFixedRangeByList[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XRandomMorphismWithFixedRangeByList[110X.     [23XF:     (     B,    L    )    \mapsto
  \mathtt{RandomMorphismWithFixedRangeByList}(B, L)[123X.[133X
  
  [1X7.6-208 AddRandomMorphismWithFixedSourceAndRangeByInteger[101X
  
  [33X[1;0Y[29X[2XAddRandomMorphismWithFixedSourceAndRangeByInteger[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XRandomMorphismWithFixedSourceAndRangeByInteger[110X.  [23XF:  (  A,  B,  n  ) \mapsto
  \mathtt{RandomMorphismWithFixedSourceAndRangeByInteger}(A, B, n)[123X.[133X
  
  [1X7.6-209 AddRandomMorphismWithFixedSourceAndRangeByList[101X
  
  [33X[1;0Y[29X[2XAddRandomMorphismWithFixedSourceAndRangeByList[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XRandomMorphismWithFixedSourceAndRangeByList[110X.   [23XF:   (  A,  B,  L  )  \mapsto
  \mathtt{RandomMorphismWithFixedSourceAndRangeByList}(A, B, L)[123X.[133X
  
  [1X7.6-210 AddRandomMorphismWithFixedSourceByInteger[101X
  
  [33X[1;0Y[29X[2XAddRandomMorphismWithFixedSourceByInteger[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XRandomMorphismWithFixedSourceByInteger[110X.    [23XF:    (    A,    n    )   \mapsto
  \mathtt{RandomMorphismWithFixedSourceByInteger}(A, n)[123X.[133X
  
  [1X7.6-211 AddRandomMorphismWithFixedSourceByList[101X
  
  [33X[1;0Y[29X[2XAddRandomMorphismWithFixedSourceByList[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XRandomMorphismWithFixedSourceByList[110X.     [23XF:     (    A,    L    )    \mapsto
  \mathtt{RandomMorphismWithFixedSourceByList}(A, L)[123X.[133X
  
  [1X7.6-212 AddRandomObjectByInteger[101X
  
  [33X[1;0Y[29X[2XAddRandomObjectByInteger[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XRandomObjectByInteger[110X. [23XF: ( n ) \mapsto \mathtt{RandomObjectByInteger}(n)[123X.[133X
  
  [1X7.6-213 AddRandomObjectByList[101X
  
  [33X[1;0Y[29X[2XAddRandomObjectByList[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given function [23XF[123X to the category for the basic operation [10XRandomObjectByList[110X.
  [23XF: ( L ) \mapsto \mathtt{RandomObjectByList}(L)[123X.[133X
  
  [1X7.6-214 AddSimplifyEndo[101X
  
  [33X[1;0Y[29X[2XAddSimplifyEndo[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given  function [23XF[123X to the category for the basic operation [10XSimplifyEndo[110X. [23XF: (
  mor, n ) \mapsto \mathtt{SimplifyEndo}(mor, n)[123X.[133X
  
  [1X7.6-215 AddSimplifyEndo_IsoFromInputObject[101X
  
  [33X[1;0Y[29X[2XAddSimplifyEndo_IsoFromInputObject[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XSimplifyEndo_IsoFromInputObject[110X.     [23XF:     (     mor,     n    )    \mapsto
  \mathtt{SimplifyEndo_IsoFromInputObject}(mor, n)[123X.[133X
  
  [1X7.6-216 AddSimplifyEndo_IsoToInputObject[101X
  
  [33X[1;0Y[29X[2XAddSimplifyEndo_IsoToInputObject[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XSimplifyEndo_IsoToInputObject[110X.     [23XF:     (     mor,     n     )     \mapsto
  \mathtt{SimplifyEndo_IsoToInputObject}(mor, n)[123X.[133X
  
  [1X7.6-217 AddSimplifyMorphism[101X
  
  [33X[1;0Y[29X[2XAddSimplifyMorphism[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given  function  [23XF[123X to the category for the basic operation [10XSimplifyMorphism[110X.
  [23XF: ( mor, n ) \mapsto \mathtt{SimplifyMorphism}(mor, n)[123X.[133X
  
  [1X7.6-218 AddSimplifyObject[101X
  
  [33X[1;0Y[29X[2XAddSimplifyObject[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given  function [23XF[123X to the category for the basic operation [10XSimplifyObject[110X. [23XF:
  ( A, n ) \mapsto \mathtt{SimplifyObject}(A, n)[123X.[133X
  
  [1X7.6-219 AddSimplifyObject_IsoFromInputObject[101X
  
  [33X[1;0Y[29X[2XAddSimplifyObject_IsoFromInputObject[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XSimplifyObject_IsoFromInputObject[110X.     [23XF:     (     A,     n    )    \mapsto
  \mathtt{SimplifyObject_IsoFromInputObject}(A, n)[123X.[133X
  
  [1X7.6-220 AddSimplifyObject_IsoToInputObject[101X
  
  [33X[1;0Y[29X[2XAddSimplifyObject_IsoToInputObject[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XSimplifyObject_IsoToInputObject[110X.     [23XF:     (     A,     n     )     \mapsto
  \mathtt{SimplifyObject_IsoToInputObject}(A, n)[123X.[133X
  
  [1X7.6-221 AddSimplifyRange[101X
  
  [33X[1;0Y[29X[2XAddSimplifyRange[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given function [23XF[123X to the category for the basic operation [10XSimplifyRange[110X. [23XF: (
  mor, n ) \mapsto \mathtt{SimplifyRange}(mor, n)[123X.[133X
  
  [1X7.6-222 AddSimplifyRange_IsoFromInputObject[101X
  
  [33X[1;0Y[29X[2XAddSimplifyRange_IsoFromInputObject[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XSimplifyRange_IsoFromInputObject[110X.     [23XF:     (     mor,    n    )    \mapsto
  \mathtt{SimplifyRange_IsoFromInputObject}(mor, n)[123X.[133X
  
  [1X7.6-223 AddSimplifyRange_IsoToInputObject[101X
  
  [33X[1;0Y[29X[2XAddSimplifyRange_IsoToInputObject[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XSimplifyRange_IsoToInputObject[110X.     [23XF:     (     mor,     n     )    \mapsto
  \mathtt{SimplifyRange_IsoToInputObject}(mor, n)[123X.[133X
  
  [1X7.6-224 AddSimplifySource[101X
  
  [33X[1;0Y[29X[2XAddSimplifySource[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given  function [23XF[123X to the category for the basic operation [10XSimplifySource[110X. [23XF:
  ( mor, n ) \mapsto \mathtt{SimplifySource}(mor, n)[123X.[133X
  
  [1X7.6-225 AddSimplifySourceAndRange[101X
  
  [33X[1;0Y[29X[2XAddSimplifySourceAndRange[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XSimplifySourceAndRange[110X.       [23XF:      (      mor,      n      )      \mapsto
  \mathtt{SimplifySourceAndRange}(mor, n)[123X.[133X
  
  [1X7.6-226 AddSimplifySourceAndRange_IsoFromInputRange[101X
  
  [33X[1;0Y[29X[2XAddSimplifySourceAndRange_IsoFromInputRange[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XSimplifySourceAndRange_IsoFromInputRange[110X.    [23XF:   (   mor,   n   )   \mapsto
  \mathtt{SimplifySourceAndRange_IsoFromInputRange}(mor, n)[123X.[133X
  
  [1X7.6-227 AddSimplifySourceAndRange_IsoFromInputSource[101X
  
  [33X[1;0Y[29X[2XAddSimplifySourceAndRange_IsoFromInputSource[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XSimplifySourceAndRange_IsoFromInputSource[110X.   [23XF:   (   mor,   n   )   \mapsto
  \mathtt{SimplifySourceAndRange_IsoFromInputSource}(mor, n)[123X.[133X
  
  [1X7.6-228 AddSimplifySourceAndRange_IsoToInputRange[101X
  
  [33X[1;0Y[29X[2XAddSimplifySourceAndRange_IsoToInputRange[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XSimplifySourceAndRange_IsoToInputRange[110X.    [23XF:    (    mor,   n   )   \mapsto
  \mathtt{SimplifySourceAndRange_IsoToInputRange}(mor, n)[123X.[133X
  
  [1X7.6-229 AddSimplifySourceAndRange_IsoToInputSource[101X
  
  [33X[1;0Y[29X[2XAddSimplifySourceAndRange_IsoToInputSource[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XSimplifySourceAndRange_IsoToInputSource[110X.    [23XF:    (   mor,   n   )   \mapsto
  \mathtt{SimplifySourceAndRange_IsoToInputSource}(mor, n)[123X.[133X
  
  [1X7.6-230 AddSimplifySource_IsoFromInputObject[101X
  
  [33X[1;0Y[29X[2XAddSimplifySource_IsoFromInputObject[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XSimplifySource_IsoFromInputObject[110X.     [23XF:     (    mor,    n    )    \mapsto
  \mathtt{SimplifySource_IsoFromInputObject}(mor, n)[123X.[133X
  
  [1X7.6-231 AddSimplifySource_IsoToInputObject[101X
  
  [33X[1;0Y[29X[2XAddSimplifySource_IsoToInputObject[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XSimplifySource_IsoToInputObject[110X.     [23XF:     (     mor,     n    )    \mapsto
  \mathtt{SimplifySource_IsoToInputObject}(mor, n)[123X.[133X
  
  [1X7.6-232 AddSolveLinearSystemInAbCategory[101X
  
  [33X[1;0Y[29X[2XAddSolveLinearSystemInAbCategory[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XSolveLinearSystemInAbCategory[110X.   [23XF:   (   arg2,   arg3,   arg4   )   \mapsto
  \mathtt{SolveLinearSystemInAbCategory}(arg2, arg3, arg4)[123X.[133X
  
  [1X7.6-233 AddSolveLinearSystemInAbCategoryOrFail[101X
  
  [33X[1;0Y[29X[2XAddSolveLinearSystemInAbCategoryOrFail[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XSolveLinearSystemInAbCategoryOrFail[110X.   [23XF:  (  arg2,  arg3,  arg4  )  \mapsto
  \mathtt{SolveLinearSystemInAbCategoryOrFail}(arg2, arg3, arg4)[123X.[133X
  
  [1X7.6-234 AddSomeInjectiveObject[101X
  
  [33X[1;0Y[29X[2XAddSomeInjectiveObject[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XSomeInjectiveObject[110X. [23XF: ( arg2 ) \mapsto \mathtt{SomeInjectiveObject}(arg2)[123X.[133X
  
  [1X7.6-235 AddSomeProjectiveObject[101X
  
  [33X[1;0Y[29X[2XAddSomeProjectiveObject[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XSomeProjectiveObject[110X.        [23XF:        (        arg2        )        \mapsto
  \mathtt{SomeProjectiveObject}(arg2)[123X.[133X
  
  [1X7.6-236 AddSomeReductionBySplitEpiSummand[101X
  
  [33X[1;0Y[29X[2XAddSomeReductionBySplitEpiSummand[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XSomeReductionBySplitEpiSummand[110X.      [23XF:      (      alpha      )     \mapsto
  \mathtt{SomeReductionBySplitEpiSummand}(alpha)[123X.[133X
  
  [1X7.6-237 AddSomeReductionBySplitEpiSummand_MorphismFromInputRange[101X
  
  [33X[1;0Y[29X[2XAddSomeReductionBySplitEpiSummand_MorphismFromInputRange[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XSomeReductionBySplitEpiSummand_MorphismFromInputRange[110X.  [23XF: ( alpha ) \mapsto
  \mathtt{SomeReductionBySplitEpiSummand_MorphismFromInputRange}(alpha)[123X.[133X
  
  [1X7.6-238 AddSomeReductionBySplitEpiSummand_MorphismToInputRange[101X
  
  [33X[1;0Y[29X[2XAddSomeReductionBySplitEpiSummand_MorphismToInputRange[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XSomeReductionBySplitEpiSummand_MorphismToInputRange[110X.  [23XF:  (  alpha ) \mapsto
  \mathtt{SomeReductionBySplitEpiSummand_MorphismToInputRange}(alpha)[123X.[133X
  
  [1X7.6-239 AddSubtractionForMorphisms[101X
  
  [33X[1;0Y[29X[2XAddSubtractionForMorphisms[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XSubtractionForMorphisms[110X.       [23XF:       (      a,      b      )      \mapsto
  \mathtt{SubtractionForMorphisms}(a, b)[123X.[133X
  
  [1X7.6-240 AddSumOfMorphisms[101X
  
  [33X[1;0Y[29X[2XAddSumOfMorphisms[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given  function [23XF[123X to the category for the basic operation [10XSumOfMorphisms[110X. [23XF:
  ( source, list_of_morphisms, range ) \mapsto \mathtt{SumOfMorphisms}(source,
  list_of_morphisms, range)[123X.[133X
  
  [1X7.6-241 AddTerminalObject[101X
  
  [33X[1;0Y[29X[2XAddTerminalObject[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given  function [23XF[123X to the category for the basic operation [10XTerminalObject[110X. [23XF:
  ( ) \mapsto \mathtt{TerminalObject}()[123X.[133X
  
  [1X7.6-242 AddTerminalObjectFunctorial[101X
  
  [33X[1;0Y[29X[2XAddTerminalObjectFunctorial[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XTerminalObjectFunctorial[110X.          [23XF:          (          )          \mapsto
  \mathtt{TerminalObjectFunctorial}()[123X.[133X
  
  [1X7.6-243 AddTerminalObjectFunctorialWithGivenTerminalObjects[101X
  
  [33X[1;0Y[29X[2XAddTerminalObjectFunctorialWithGivenTerminalObjects[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XTerminalObjectFunctorialWithGivenTerminalObjects[110X.  [23XF:  (  P,  Pp  )  \mapsto
  \mathtt{TerminalObjectFunctorialWithGivenTerminalObjects}(P, Pp)[123X.[133X
  
  [1X7.6-244 AddUniversalMorphismFromCoequalizer[101X
  
  [33X[1;0Y[29X[2XAddUniversalMorphismFromCoequalizer[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XUniversalMorphismFromCoequalizer[110X.  [23XF:  (  Y,  morphisms,  T,  tau  ) \mapsto
  \mathtt{UniversalMorphismFromCoequalizer}(Y, morphisms, T, tau)[123X.[133X
  
  [1X7.6-245 AddUniversalMorphismFromCoequalizerWithGivenCoequalizer[101X
  
  [33X[1;0Y[29X[2XAddUniversalMorphismFromCoequalizerWithGivenCoequalizer[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XUniversalMorphismFromCoequalizerWithGivenCoequalizer[110X.  [23XF: ( Y, morphisms, T,
  tau,                     P                     )                     \mapsto
  \mathtt{UniversalMorphismFromCoequalizerWithGivenCoequalizer}(Y,  morphisms,
  T, tau, P)[123X.[133X
  
  [1X7.6-246 AddUniversalMorphismFromCoproduct[101X
  
  [33X[1;0Y[29X[2XAddUniversalMorphismFromCoproduct[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XUniversalMorphismFromCoproduct[110X.   [23XF:   (   objects,   T,   tau   )   \mapsto
  \mathtt{UniversalMorphismFromCoproduct}(objects, T, tau)[123X.[133X
  
  [1X7.6-247 AddUniversalMorphismFromCoproductWithGivenCoproduct[101X
  
  [33X[1;0Y[29X[2XAddUniversalMorphismFromCoproductWithGivenCoproduct[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XUniversalMorphismFromCoproductWithGivenCoproduct[110X.  [23XF: ( objects, T, tau, P )
  \mapsto   \mathtt{UniversalMorphismFromCoproductWithGivenCoproduct}(objects,
  T, tau, P)[123X.[133X
  
  [1X7.6-248 AddUniversalMorphismFromDirectSum[101X
  
  [33X[1;0Y[29X[2XAddUniversalMorphismFromDirectSum[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XUniversalMorphismFromDirectSum[110X.   [23XF:   (   objects,   T,   tau   )   \mapsto
  \mathtt{UniversalMorphismFromDirectSum}(objects, T, tau)[123X.[133X
  
  [1X7.6-249 AddUniversalMorphismFromDirectSumWithGivenDirectSum[101X
  
  [33X[1;0Y[29X[2XAddUniversalMorphismFromDirectSumWithGivenDirectSum[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XUniversalMorphismFromDirectSumWithGivenDirectSum[110X.  [23XF: ( objects, T, tau, P )
  \mapsto   \mathtt{UniversalMorphismFromDirectSumWithGivenDirectSum}(objects,
  T, tau, P)[123X.[133X
  
  [1X7.6-250 AddUniversalMorphismFromImage[101X
  
  [33X[1;0Y[29X[2XAddUniversalMorphismFromImage[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XUniversalMorphismFromImage[110X.     [23XF:     (     alpha,     tau     )    \mapsto
  \mathtt{UniversalMorphismFromImage}(alpha, tau)[123X.[133X
  
  [1X7.6-251 AddUniversalMorphismFromImageWithGivenImageObject[101X
  
  [33X[1;0Y[29X[2XAddUniversalMorphismFromImageWithGivenImageObject[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XUniversalMorphismFromImageWithGivenImageObject[110X. [23XF: ( alpha, tau, I ) \mapsto
  \mathtt{UniversalMorphismFromImageWithGivenImageObject}(alpha, tau, I)[123X.[133X
  
  [1X7.6-252 AddUniversalMorphismFromInitialObject[101X
  
  [33X[1;0Y[29X[2XAddUniversalMorphismFromInitialObject[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XUniversalMorphismFromInitialObject[110X.      [23XF:      (      T      )     \mapsto
  \mathtt{UniversalMorphismFromInitialObject}(T)[123X.[133X
  
  [1X7.6-253 AddUniversalMorphismFromInitialObjectWithGivenInitialObject[101X
  
  [33X[1;0Y[29X[2XAddUniversalMorphismFromInitialObjectWithGivenInitialObject[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XUniversalMorphismFromInitialObjectWithGivenInitialObject[110X.   [23XF:   (  T,  P  )
  \mapsto \mathtt{UniversalMorphismFromInitialObjectWithGivenInitialObject}(T,
  P)[123X.[133X
  
  [1X7.6-254 AddUniversalMorphismFromPushout[101X
  
  [33X[1;0Y[29X[2XAddUniversalMorphismFromPushout[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XUniversalMorphismFromPushout[110X.   [23XF:   (   morphisms,   T,   tau   )   \mapsto
  \mathtt{UniversalMorphismFromPushout}(morphisms, T, tau)[123X.[133X
  
  [1X7.6-255 AddUniversalMorphismFromPushoutWithGivenPushout[101X
  
  [33X[1;0Y[29X[2XAddUniversalMorphismFromPushoutWithGivenPushout[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XUniversalMorphismFromPushoutWithGivenPushout[110X.  [23XF:  (  morphisms, T, tau, P )
  \mapsto  \mathtt{UniversalMorphismFromPushoutWithGivenPushout}(morphisms, T,
  tau, P)[123X.[133X
  
  [1X7.6-256 AddUniversalMorphismFromZeroObject[101X
  
  [33X[1;0Y[29X[2XAddUniversalMorphismFromZeroObject[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XUniversalMorphismFromZeroObject[110X.       [23XF:       (      T      )      \mapsto
  \mathtt{UniversalMorphismFromZeroObject}(T)[123X.[133X
  
  [1X7.6-257 AddUniversalMorphismFromZeroObjectWithGivenZeroObject[101X
  
  [33X[1;0Y[29X[2XAddUniversalMorphismFromZeroObjectWithGivenZeroObject[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XUniversalMorphismFromZeroObjectWithGivenZeroObject[110X.  [23XF:  (  T,  P  ) \mapsto
  \mathtt{UniversalMorphismFromZeroObjectWithGivenZeroObject}(T, P)[123X.[133X
  
  [1X7.6-258 AddUniversalMorphismIntoCoimage[101X
  
  [33X[1;0Y[29X[2XAddUniversalMorphismIntoCoimage[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XUniversalMorphismIntoCoimage[110X.     [23XF:     (     alpha,    tau    )    \mapsto
  \mathtt{UniversalMorphismIntoCoimage}(alpha, tau)[123X.[133X
  
  [1X7.6-259 AddUniversalMorphismIntoCoimageWithGivenCoimageObject[101X
  
  [33X[1;0Y[29X[2XAddUniversalMorphismIntoCoimageWithGivenCoimageObject[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XUniversalMorphismIntoCoimageWithGivenCoimageObject[110X.  [23XF:  (  alpha,  tau, C )
  \mapsto   \mathtt{UniversalMorphismIntoCoimageWithGivenCoimageObject}(alpha,
  tau, C)[123X.[133X
  
  [1X7.6-260 AddUniversalMorphismIntoDirectProduct[101X
  
  [33X[1;0Y[29X[2XAddUniversalMorphismIntoDirectProduct[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XUniversalMorphismIntoDirectProduct[110X.   [23XF:   (   objects,  T,  tau  )  \mapsto
  \mathtt{UniversalMorphismIntoDirectProduct}(objects, T, tau)[123X.[133X
  
  [1X7.6-261 AddUniversalMorphismIntoDirectProductWithGivenDirectProduct[101X
  
  [33X[1;0Y[29X[2XAddUniversalMorphismIntoDirectProductWithGivenDirectProduct[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XUniversalMorphismIntoDirectProductWithGivenDirectProduct[110X.  [23XF:  ( objects, T,
  tau,                     P                     )                     \mapsto
  \mathtt{UniversalMorphismIntoDirectProductWithGivenDirectProduct}(objects,
  T, tau, P)[123X.[133X
  
  [1X7.6-262 AddUniversalMorphismIntoDirectSum[101X
  
  [33X[1;0Y[29X[2XAddUniversalMorphismIntoDirectSum[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XUniversalMorphismIntoDirectSum[110X.   [23XF:   (   objects,   T,   tau   )   \mapsto
  \mathtt{UniversalMorphismIntoDirectSum}(objects, T, tau)[123X.[133X
  
  [1X7.6-263 AddUniversalMorphismIntoDirectSumWithGivenDirectSum[101X
  
  [33X[1;0Y[29X[2XAddUniversalMorphismIntoDirectSumWithGivenDirectSum[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XUniversalMorphismIntoDirectSumWithGivenDirectSum[110X.  [23XF: ( objects, T, tau, P )
  \mapsto   \mathtt{UniversalMorphismIntoDirectSumWithGivenDirectSum}(objects,
  T, tau, P)[123X.[133X
  
  [1X7.6-264 AddUniversalMorphismIntoEqualizer[101X
  
  [33X[1;0Y[29X[2XAddUniversalMorphismIntoEqualizer[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XUniversalMorphismIntoEqualizer[110X.   [23XF:  (  Y,  morphisms,  T,  tau  )  \mapsto
  \mathtt{UniversalMorphismIntoEqualizer}(Y, morphisms, T, tau)[123X.[133X
  
  [1X7.6-265 AddUniversalMorphismIntoEqualizerWithGivenEqualizer[101X
  
  [33X[1;0Y[29X[2XAddUniversalMorphismIntoEqualizerWithGivenEqualizer[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XUniversalMorphismIntoEqualizerWithGivenEqualizer[110X. [23XF: ( Y, morphisms, T, tau,
  P   )  \mapsto  \mathtt{UniversalMorphismIntoEqualizerWithGivenEqualizer}(Y,
  morphisms, T, tau, P)[123X.[133X
  
  [1X7.6-266 AddUniversalMorphismIntoFiberProduct[101X
  
  [33X[1;0Y[29X[2XAddUniversalMorphismIntoFiberProduct[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XUniversalMorphismIntoFiberProduct[110X.   [23XF:   (  morphisms,  T,  tau  )  \mapsto
  \mathtt{UniversalMorphismIntoFiberProduct}(morphisms, T, tau)[123X.[133X
  
  [1X7.6-267 AddUniversalMorphismIntoFiberProductWithGivenFiberProduct[101X
  
  [33X[1;0Y[29X[2XAddUniversalMorphismIntoFiberProductWithGivenFiberProduct[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XUniversalMorphismIntoFiberProductWithGivenFiberProduct[110X.  [23XF:  ( morphisms, T,
  tau,                     P                     )                     \mapsto
  \mathtt{UniversalMorphismIntoFiberProductWithGivenFiberProduct}(morphisms,
  T, tau, P)[123X.[133X
  
  [1X7.6-268 AddUniversalMorphismIntoTerminalObject[101X
  
  [33X[1;0Y[29X[2XAddUniversalMorphismIntoTerminalObject[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XUniversalMorphismIntoTerminalObject[110X.      [23XF:      (      T     )     \mapsto
  \mathtt{UniversalMorphismIntoTerminalObject}(T)[123X.[133X
  
  [1X7.6-269 AddUniversalMorphismIntoTerminalObjectWithGivenTerminalObject[101X
  
  [33X[1;0Y[29X[2XAddUniversalMorphismIntoTerminalObjectWithGivenTerminalObject[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XUniversalMorphismIntoTerminalObjectWithGivenTerminalObject[110X.  [23XF:  (  T,  P  )
  \mapsto
  \mathtt{UniversalMorphismIntoTerminalObjectWithGivenTerminalObject}(T, P)[123X.[133X
  
  [1X7.6-270 AddUniversalMorphismIntoZeroObject[101X
  
  [33X[1;0Y[29X[2XAddUniversalMorphismIntoZeroObject[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XUniversalMorphismIntoZeroObject[110X.       [23XF:       (      T      )      \mapsto
  \mathtt{UniversalMorphismIntoZeroObject}(T)[123X.[133X
  
  [1X7.6-271 AddUniversalMorphismIntoZeroObjectWithGivenZeroObject[101X
  
  [33X[1;0Y[29X[2XAddUniversalMorphismIntoZeroObjectWithGivenZeroObject[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XUniversalMorphismIntoZeroObjectWithGivenZeroObject[110X.  [23XF:  (  T,  P  ) \mapsto
  \mathtt{UniversalMorphismIntoZeroObjectWithGivenZeroObject}(T, P)[123X.[133X
  
  [1X7.6-272 AddVerticalPostCompose[101X
  
  [33X[1;0Y[29X[2XAddVerticalPostCompose[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XVerticalPostCompose[110X.      [23XF:      (      arg2,      arg3      )      \mapsto
  \mathtt{VerticalPostCompose}(arg2, arg3)[123X.[133X
  
  [1X7.6-273 AddVerticalPreCompose[101X
  
  [33X[1;0Y[29X[2XAddVerticalPreCompose[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given function [23XF[123X to the category for the basic operation [10XVerticalPreCompose[110X.
  [23XF: ( arg2, arg3 ) \mapsto \mathtt{VerticalPreCompose}(arg2, arg3)[123X.[133X
  
  [1X7.6-274 AddZeroMorphism[101X
  
  [33X[1;0Y[29X[2XAddZeroMorphism[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given  function [23XF[123X to the category for the basic operation [10XZeroMorphism[110X. [23XF: (
  a, b ) \mapsto \mathtt{ZeroMorphism}(a, b)[123X.[133X
  
  [1X7.6-275 AddZeroObject[101X
  
  [33X[1;0Y[29X[2XAddZeroObject[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given  function [23XF[123X to the category for the basic operation [10XZeroObject[110X. [23XF: ( )
  \mapsto \mathtt{ZeroObject}()[123X.[133X
  
  [1X7.6-276 AddZeroObjectFunctorial[101X
  
  [33X[1;0Y[29X[2XAddZeroObjectFunctorial[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XZeroObjectFunctorial[110X. [23XF: ( ) \mapsto \mathtt{ZeroObjectFunctorial}()[123X.[133X
  
  [1X7.6-277 AddZeroObjectFunctorialWithGivenZeroObjects[101X
  
  [33X[1;0Y[29X[2XAddZeroObjectFunctorialWithGivenZeroObjects[102X( [3XC[103X, [3XF[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YThe  arguments  are  a  category [23XC[123X and a function [23XF[123X. This operation adds the
  given    function    [23XF[123X   to   the   category   for   the   basic   operation
  [10XZeroObjectFunctorialWithGivenZeroObjects[110X.    [23XF:    (   P,   Pp   )   \mapsto
  \mathtt{ZeroObjectFunctorialWithGivenZeroObjects}(P, Pp)[123X.[133X
  
