  
  
                                     [1X CAP [101X
  
  
                     [1X Categories, Algorithms, Programming [101X
  
  
                                   2022.12-11
  
  
                                16 December 2022
  
  
                               Sebastian Gutsche
  
                                Sebastian Posur
  
                            Øystein Skartsæterhagen
  
  
  
  Sebastian Gutsche
      Email:    [7Xmailto:gutsche@mathematik.uni-siegen.de[107X
      Homepage: [7Xhttps://sebasguts.github.io/[107X
      Address:  [33X[0;14YDepartment Mathematik[133X
                [33X[0;14YUniversität Siegen[133X
                [33X[0;14YWalter-Flex-Straße 3[133X
                [33X[0;14Y57068 Siegen[133X
                [33X[0;14YGermany[133X
  
  
  Sebastian Posur
      Email:    [7Xmailto:sebastian.posur@uni-siegen.de[107X
      Homepage: [7Xhttps://sebastianpos.github.io[107X
      Address:  [33X[0;14YDepartment Mathematik[133X
                [33X[0;14YUniversität Siegen[133X
                [33X[0;14YWalter-Flex-Straße 3[133X
                [33X[0;14Y57068 Siegen[133X
                [33X[0;14YGermany[133X
  
  
  Øystein Skartsæterhagen
      Email:    [7Xmailto:oysteini@math.ntnu.no[107X
      Homepage: [7Xhttp://www.math.ntnu.no/~oysteini/[107X
      Address:  [33X[0;14YNTNU[133X
                [33X[0;14YInstitutt for matematiske fag[133X
                [33X[0;14Y7491 Trondheim[133X
                [33X[0;14YNorway[133X
  
  
  
  -------------------------------------------------------
  
  
  [1XContents (CAP)[101X
  
  1 [33X[0;0YCAP Categories[133X
    1.1 [33X[0;0YCategories[133X
      1.1-1 IsCapCategory
      1.1-2 IsCapCategoryCell
      1.1-3 IsCapCategoryObject
      1.1-4 IsCapCategoryMorphism
      1.1-5 IsCapCategoryTwoCell
    1.2 [33X[0;0YCategorical properties[133X
      1.2-1 AddCategoricalProperty
      1.2-2 IsEquippedWithHomomorphismStructure
      1.2-3 IsCategoryWithDecidableLifts
      1.2-4 IsCategoryWithDecidableColifts
      1.2-5 IsEnrichedOverCommutativeRegularSemigroup
      1.2-6 IsSkeletalCategory
      1.2-7 IsAbCategory
      1.2-8 IsLinearCategoryOverCommutativeRing
      1.2-9 IsAdditiveCategory
      1.2-10 IsPreAbelianCategory
      1.2-11 IsAbelianCategory
      1.2-12 IsAbelianCategoryWithEnoughProjectives
      1.2-13 IsAbelianCategoryWithEnoughInjectives
      1.2-14 IsLocallyOfFiniteProjectiveDimension
      1.2-15 IsLocallyOfFiniteInjectiveDimension
    1.3 [33X[0;0YConstructor[133X
      1.3-1 CreateCapCategory
      1.3-2 CreateCapCategory
      1.3-3 CreateCapCategory
      1.3-4 CreateCapCategoryWithDataTypes
    1.4 [33X[0;0YInternal Attributes[133X
      1.4-1 Name
      1.4-2 CategoryFilter
      1.4-3 ObjectFilter
      1.4-4 MorphismFilter
      1.4-5 TwoCellFilter
      1.4-6 ObjectDatumType
      1.4-7 MorphismDatumType
      1.4-8 TwoCellDatumType
      1.4-9 CommutativeRingOfLinearCategory
      1.4-10 RangeCategoryOfHomomorphismStructure
      1.4-11 AdditiveGenerators
      1.4-12 IndecomposableProjectiveObjects
      1.4-13 IndecomposableInjectiveObjects
    1.5 [33X[0;0YLogic switcher[133X
      1.5-1 CapCategorySwitchLogicPropagationForObjectsOn
      1.5-2 CapCategorySwitchLogicPropagationForObjectsOff
      1.5-3 CapCategorySwitchLogicPropagationForMorphismsOn
      1.5-4 CapCategorySwitchLogicPropagationForMorphismsOff
      1.5-5 CapCategorySwitchLogicPropagationOn
      1.5-6 CapCategorySwitchLogicPropagationOff
      1.5-7 CapCategorySwitchLogicOn
      1.5-8 CapCategorySwitchLogicOff
    1.6 [33X[0;0YTool functions[133X
      1.6-1 CanCompute
      1.6-2 CheckConstructivenessOfCategory
    1.7 [33X[0;0YWell-Definedness of Cells[133X
      1.7-1 IsWellDefined
    1.8 [33X[0;0YUnpacking data structures[133X
      1.8-1 Down
      1.8-2 DownOnlyMorphismData
      1.8-3 DownToBottom
    1.9 [33X[0;0YCaching[133X
      1.9-1 SetCachingOfCategory
      1.9-2 SetCachingOfCategoryWeak
      1.9-3 SetDefaultCaching
    1.10 [33X[0;0YSanity checks[133X
      1.10-1 DisableInputSanityChecks
    1.11 [33X[0;0YTiming statistics[133X
      1.11-1 EnableTimingStatistics
    1.12 [33X[0;0YEnable automatic calls of [10XAdd[110X[133X
      1.12-1 EnableAddForCategoricalOperations
    1.13 [33X[0;0YPerformance tweaks[133X
    1.14 [33X[0;0YLaTeX[133X
      1.14-1 LaTeXOutput
      1.14-2 LaTeXOutput
  2 [33X[0;0YObjects[133X
    2.1 [33X[0;0YAttributes for the Type of Objects[133X
      2.1-1 CapCategory
    2.2 [33X[0;0YEquality for Objects[133X
      2.2-1 IsEqualForObjects
    2.3 [33X[0;0YCategorical Properties of Objects[133X
      2.3-1 IsBijectiveObject
      2.3-2 IsProjective
      2.3-3 IsInjective
      2.3-4 IsTerminal
      2.3-5 IsInitial
      2.3-6 IsZeroForObjects
      2.3-7 IsZero
    2.4 [33X[0;0YRandom Objects[133X
      2.4-1 RandomObjectByInteger
      2.4-2 RandomObjectByList
      2.4-3 RandomObject
      2.4-4 RandomObject
    2.5 [33X[0;0YTool functions for caches[133X
      2.5-1 IsEqualForCacheForObjects
    2.6 [33X[0;0YAdding Objects to a Category[133X
      2.6-1 Add
      2.6-2 AddObject
      2.6-3 AddObjectRepresentation
      2.6-4 ObjectifyObjectForCAPWithAttributes
      2.6-5 CreateCapCategoryObjectWithAttributes
    2.7 [33X[0;0YObject constructors[133X
      2.7-1 ObjectConstructor
      2.7-2 /
      2.7-3 ObjectDatum
    2.8 [33X[0;0YWell-Definedness of Objects[133X
      2.8-1 IsWellDefinedForObjects
    2.9 [33X[0;0YProjectives[133X
      2.9-1 SomeProjectiveObject
      2.9-2 EpimorphismFromSomeProjectiveObject
      2.9-3 EpimorphismFromSomeProjectiveObjectWithGivenSomeProjectiveObject
      2.9-4 ProjectiveLift
    2.10 [33X[0;0YInjectives[133X
      2.10-1 SomeInjectiveObject
      2.10-2 MonomorphismIntoSomeInjectiveObject
      2.10-3 MonomorphismIntoSomeInjectiveObjectWithGivenSomeInjectiveObject
      2.10-4 InjectiveColift
    2.11 [33X[0;0YSimplified Objects[133X
      2.11-1 Simplify
      2.11-2 SimplifyObject
      2.11-3 SimplifyObject_IsoFromInputObject
      2.11-4 SimplifyObject_IsoToInputObject
    2.12 [33X[0;0YDimensions[133X
      2.12-1 ProjectiveDimension
      2.12-2 InjectiveDimension
  3 [33X[0;0YMorphisms[133X
    3.1 [33X[0;0YAttributes for the Type of Morphisms[133X
      3.1-1 CapCategory
      3.1-2 Source
      3.1-3 Range
    3.2 [33X[0;0YMorphism constructors[133X
      3.2-1 MorphismConstructor
      3.2-2 MorphismDatum
    3.3 [33X[0;0YCategorical Properties of Morphisms[133X
      3.3-1 IsMonomorphism
      3.3-2 IsEpimorphism
      3.3-3 IsIsomorphism
      3.3-4 IsSplitMonomorphism
      3.3-5 IsSplitEpimorphism
      3.3-6 IsOne
      3.3-7 IsIdempotent
    3.4 [33X[0;0YRandom Morphisms[133X
      3.4-1 RandomMorphismWithFixedSourceByInteger
      3.4-2 RandomMorphismWithFixedSourceByList
      3.4-3 RandomMorphismWithFixedRangeByInteger
      3.4-4 RandomMorphismWithFixedRangeByList
      3.4-5 RandomMorphismWithFixedSourceAndRangeByInteger
      3.4-6 RandomMorphismWithFixedSourceAndRangeByList
      3.4-7 RandomMorphismByInteger
      3.4-8 RandomMorphismByList
      3.4-9 RandomMorphismWithFixedSource
    3.5 [33X[0;0YNon-Categorical Properties of Morphisms[133X
      3.5-1 IsEqualToIdentityMorphism
      3.5-2 IsEqualToZeroMorphism
      3.5-3 IsEndomorphism
      3.5-4 IsAutomorphism
    3.6 [33X[0;0YAdding Morphisms to a Category[133X
      3.6-1 Add
      3.6-2 AddMorphism
      3.6-3 AddMorphismRepresentation
      3.6-4 ObjectifyMorphismWithSourceAndRangeForCAPWithAttributes
      3.6-5 CreateCapCategoryMorphismWithAttributes
    3.7 [33X[0;0YEquality and Congruence for Morphisms[133X
      3.7-1 IsCongruentForMorphisms
      3.7-2 IsEqualForMorphisms
      3.7-3 IsEqualForMorphismsOnMor
    3.8 [33X[0;0YBasic Operations for Morphisms in Ab-Categories[133X
      3.8-1 IsZeroForMorphisms
      3.8-2 AdditionForMorphisms
      3.8-3 SubtractionForMorphisms
      3.8-4 AdditiveInverseForMorphisms
      3.8-5 MultiplyWithElementOfCommutativeRingForMorphisms
      3.8-6 *
      3.8-7 ZeroMorphism
    3.9 [33X[0;0YSubobject and Factorobject Operations[133X
      3.9-1 IsEqualAsSubobjects
      3.9-2 IsEqualAsFactorobjects
      3.9-3 IsDominating
      3.9-4 IsCodominating
    3.10 [33X[0;0YIdentity Morphism and Composition of Morphisms[133X
      3.10-1 IdentityMorphism
      3.10-2 PreCompose
      3.10-3 PreCompose
      3.10-4 PreComposeList
      3.10-5 PostCompose
      3.10-6 PostCompose
      3.10-7 PostComposeList
      3.10-8 SumOfMorphisms
    3.11 [33X[0;0YWell-Definedness of Morphisms[133X
      3.11-1 IsWellDefinedForMorphisms
    3.12 [33X[0;0YLift/Colift[133X
      3.12-1 LiftAlongMonomorphism
      3.12-2 ColiftAlongEpimorphism
      3.12-3 IsLiftableAlongMonomorphism
      3.12-4 IsColiftableAlongEpimorphism
      3.12-5 Lift
      3.12-6 LiftOrFail
      3.12-7 IsLiftable
      3.12-8 Colift
      3.12-9 ColiftOrFail
      3.12-10 IsColiftable
    3.13 [33X[0;0YInverses[133X
      3.13-1 InverseForMorphisms
      3.13-2 PreInverseForMorphisms
      3.13-3 PostInverseForMorphisms
    3.14 [33X[0;0YTool functions for caches[133X
      3.14-1 IsEqualForCacheForMorphisms
    3.15 [33X[0;0YIsHomSetInhabited[133X
      3.15-1 IsHomSetInhabited
    3.16 [33X[0;0YHomomorphism structures[133X
      3.16-1 HomomorphismStructureOnObjects
      3.16-2 HomomorphismStructureOnMorphisms
      3.16-3 HomomorphismStructureOnMorphismsWithGivenObjects
      3.16-4 DistinguishedObjectOfHomomorphismStructure
      3.16-5 InterpretMorphismAsMorphismFromDistinguishedObjectToHomomorphismStructure
      3.16-6 InterpretMorphismAsMorphismFromDistinguishedObjectToHomomorphismStructureWithGivenObjects
      3.16-7 InterpretMorphismFromDistinguishedObjectToHomomorphismStructureAsMorphism
      3.16-8 SolveLinearSystemInAbCategory
      3.16-9 SolveLinearSystemInAbCategoryOrFail
      3.16-10 MereExistenceOfSolutionOfLinearSystemInAbCategory
      3.16-11 HomStructure
      3.16-12 HomStructure
      3.16-13 HomStructure
      3.16-14 HomStructure
      3.16-15 HomStructure
      3.16-16 HomStructure
      3.16-17 HomStructure
      3.16-18 ExtendRangeOfHomomorphismStructureByFullEmbedding
      3.16-19 ExtendRangeOfHomomorphismStructureByIdentityAsFullEmbedding
      3.16-20 BasisOfExternalHom
      3.16-21 CoefficientsOfMorphismWithGivenBasisOfExternalHom
      3.16-22 CoefficientsOfMorphism
    3.17 [33X[0;0YSimplified Morphisms[133X
      3.17-1 SimplifyMorphism
      3.17-2 SimplifySource
      3.17-3 SimplifySource_IsoToInputObject
      3.17-4 SimplifySource_IsoFromInputObject
      3.17-5 SimplifyRange
      3.17-6 SimplifyRange_IsoToInputObject
      3.17-7 SimplifyRange_IsoFromInputObject
      3.17-8 SimplifySourceAndRange
      3.17-9 SimplifySourceAndRange_IsoToInputRange
      3.17-10 SimplifySourceAndRange_IsoFromInputRange
      3.17-11 SimplifySourceAndRange_IsoToInputSource
      3.17-12 SimplifySourceAndRange_IsoFromInputSource
      3.17-13 SimplifyEndo
      3.17-14 SimplifyEndo_IsoToInputObject
      3.17-15 SimplifyEndo_IsoFromInputObject
      3.17-16 Simplify
    3.18 [33X[0;0YReduction by split epi summands[133X
      3.18-1 SomeReductionBySplitEpiSummand
      3.18-2 SomeReductionBySplitEpiSummand_MorphismToInputRange
      3.18-3 SomeReductionBySplitEpiSummand_MorphismFromInputRange
  4 [33X[0;0YCategory 2-Cells[133X
    4.1 [33X[0;0YAttributes for the Type of 2-Cells[133X
      4.1-1 Source
      4.1-2 Range
    4.2 [33X[0;0YIdentity 2-Cell and Composition of 2-Cells[133X
      4.2-1 IdentityTwoCell
      4.2-2 HorizontalPreCompose
      4.2-3 HorizontalPostCompose
      4.2-4 VerticalPreCompose
      4.2-5 VerticalPostCompose
    4.3 [33X[0;0YWell-Definedness for 2-Cells[133X
      4.3-1 IsWellDefinedForTwoCells
  5 [33X[0;0YCategory of Categories[133X
    5.1 [33X[0;0YThe Category Cat[133X
      5.1-1 CapCat
    5.2 [33X[0;0YCategories[133X
      5.2-1 IsCapCategoryAsCatObject
      5.2-2 IsCapFunctor
      5.2-3 IsCapNaturalTransformation
    5.3 [33X[0;0YConstructors[133X
      5.3-1 AsCatObject
      5.3-2 AsCapCategory
    5.4 [33X[0;0YFunctors[133X
      5.4-1 CapFunctor
      5.4-2 CapFunctor
      5.4-3 SourceOfFunctor
      5.4-4 RangeOfFunctor
      5.4-5 AddObjectFunction
      5.4-6 FunctorObjectOperation
      5.4-7 AddMorphismFunction
      5.4-8 FunctorMorphismOperation
      5.4-9 ApplyFunctor
      5.4-10 InputSignature
      5.4-11 InstallFunctor
      5.4-12 IdentityFunctor
      5.4-13 FunctorCanonicalizeZeroObjects
      5.4-14 NaturalIsomorphismFromIdentityToCanonicalizeZeroObjects
      5.4-15 FunctorCanonicalizeZeroMorphisms
      5.4-16 NaturalIsomorphismFromIdentityToCanonicalizeZeroMorphisms
    5.5 [33X[0;0YNatural transformations[133X
      5.5-1 Name
      5.5-2 NaturalTransformation
      5.5-3 AddNaturalTransformationFunction
      5.5-4 ApplyNaturalTransformation
      5.5-5 InstallNaturalTransformation
      5.5-6 HorizontalPreComposeNaturalTransformationWithFunctor
      5.5-7 HorizontalPreComposeFunctorWithNaturalTransformation
  6 [33X[0;0YUniversal Objects[133X
    6.1 [33X[0;0YKernel[133X
      6.1-1 KernelObject
      6.1-2 KernelEmbedding
      6.1-3 KernelEmbeddingWithGivenKernelObject
      6.1-4 MorphismFromKernelObjectToSink
      6.1-5 MorphismFromKernelObjectToSinkWithGivenKernelObject
      6.1-6 KernelLift
      6.1-7 KernelLiftWithGivenKernelObject
      6.1-8 KernelObjectFunctorial
      6.1-9 KernelObjectFunctorial
      6.1-10 KernelObjectFunctorialWithGivenKernelObjects
      6.1-11 KernelObjectFunctorialWithGivenKernelObjects
    6.2 [33X[0;0YCokernel[133X
      6.2-1 CokernelObject
      6.2-2 CokernelProjection
      6.2-3 CokernelProjectionWithGivenCokernelObject
      6.2-4 MorphismFromSourceToCokernelObject
      6.2-5 MorphismFromSourceToCokernelObjectWithGivenCokernelObject
      6.2-6 CokernelColift
      6.2-7 CokernelColiftWithGivenCokernelObject
      6.2-8 CokernelObjectFunctorial
      6.2-9 CokernelObjectFunctorial
      6.2-10 CokernelObjectFunctorialWithGivenCokernelObjects
      6.2-11 CokernelObjectFunctorialWithGivenCokernelObjects
    6.3 [33X[0;0YZero Object[133X
      6.3-1 ZeroObject
      6.3-2 ZeroObject
      6.3-3 UniversalMorphismFromZeroObject
      6.3-4 UniversalMorphismFromZeroObjectWithGivenZeroObject
      6.3-5 UniversalMorphismIntoZeroObject
      6.3-6 UniversalMorphismIntoZeroObjectWithGivenZeroObject
      6.3-7 MorphismFromZeroObject
      6.3-8 MorphismIntoZeroObject
      6.3-9 IsomorphismFromZeroObjectToInitialObject
      6.3-10 IsomorphismFromInitialObjectToZeroObject
      6.3-11 IsomorphismFromZeroObjectToTerminalObject
      6.3-12 IsomorphismFromTerminalObjectToZeroObject
      6.3-13 ZeroObjectFunctorial
      6.3-14 ZeroObjectFunctorialWithGivenZeroObjects
    6.4 [33X[0;0YTerminal Object[133X
      6.4-1 TerminalObject
      6.4-2 TerminalObject
      6.4-3 UniversalMorphismIntoTerminalObject
      6.4-4 UniversalMorphismIntoTerminalObjectWithGivenTerminalObject
      6.4-5 TerminalObjectFunctorial
      6.4-6 TerminalObjectFunctorialWithGivenTerminalObjects
    6.5 [33X[0;0YInitial Object[133X
      6.5-1 InitialObject
      6.5-2 InitialObject
      6.5-3 UniversalMorphismFromInitialObject
      6.5-4 UniversalMorphismFromInitialObjectWithGivenInitialObject
      6.5-5 InitialObjectFunctorial
      6.5-6 InitialObjectFunctorialWithGivenInitialObjects
    6.6 [33X[0;0YDirect Sum[133X
      6.6-1 DirectSum
      6.6-2 DirectSumOp
      6.6-3 ProjectionInFactorOfDirectSum
      6.6-4 ProjectionInFactorOfDirectSumWithGivenDirectSum
      6.6-5 InjectionOfCofactorOfDirectSum
      6.6-6 InjectionOfCofactorOfDirectSumWithGivenDirectSum
      6.6-7 UniversalMorphismIntoDirectSum
      6.6-8 UniversalMorphismIntoDirectSumWithGivenDirectSum
      6.6-9 UniversalMorphismFromDirectSum
      6.6-10 UniversalMorphismFromDirectSumWithGivenDirectSum
      6.6-11 IsomorphismFromDirectSumToDirectProduct
      6.6-12 IsomorphismFromDirectProductToDirectSum
      6.6-13 IsomorphismFromDirectSumToCoproduct
      6.6-14 IsomorphismFromCoproductToDirectSum
      6.6-15 MorphismBetweenDirectSums
      6.6-16 MorphismBetweenDirectSums
      6.6-17 MorphismBetweenDirectSumsWithGivenDirectSums
      6.6-18 MorphismBetweenDirectSums
      6.6-19 ComponentOfMorphismIntoDirectSum
      6.6-20 ComponentOfMorphismFromDirectSum
      6.6-21 DirectSumFunctorial
      6.6-22 DirectSumFunctorialWithGivenDirectSums
    6.7 [33X[0;0YCoproduct[133X
      6.7-1 Coproduct
      6.7-2 Coproduct
      6.7-3 Coproduct
      6.7-4 InjectionOfCofactorOfCoproduct
      6.7-5 InjectionOfCofactorOfCoproductWithGivenCoproduct
      6.7-6 UniversalMorphismFromCoproduct
      6.7-7 UniversalMorphismFromCoproductWithGivenCoproduct
      6.7-8 CoproductFunctorial
      6.7-9 CoproductFunctorialWithGivenCoproducts
    6.8 [33X[0;0YDirect Product[133X
      6.8-1 DirectProduct
      6.8-2 DirectProductOp
      6.8-3 ProjectionInFactorOfDirectProduct
      6.8-4 ProjectionInFactorOfDirectProductWithGivenDirectProduct
      6.8-5 UniversalMorphismIntoDirectProduct
      6.8-6 UniversalMorphismIntoDirectProductWithGivenDirectProduct
      6.8-7 DirectProductFunctorial
      6.8-8 DirectProductFunctorialWithGivenDirectProducts
    6.9 [33X[0;0YEqualizer[133X
      6.9-1 Equalizer
      6.9-2 EqualizerOp
      6.9-3 EmbeddingOfEqualizer
      6.9-4 EmbeddingOfEqualizerWithGivenEqualizer
      6.9-5 MorphismFromEqualizerToSink
      6.9-6 MorphismFromEqualizerToSinkWithGivenEqualizer
      6.9-7 UniversalMorphismIntoEqualizer
      6.9-8 UniversalMorphismIntoEqualizerWithGivenEqualizer
      6.9-9 EqualizerFunctorial
      6.9-10 EqualizerFunctorialWithGivenEqualizers
    6.10 [33X[0;0YCoequalizer[133X
      6.10-1 Coequalizer
      6.10-2 CoequalizerOp
      6.10-3 ProjectionOntoCoequalizer
      6.10-4 ProjectionOntoCoequalizerWithGivenCoequalizer
      6.10-5 MorphismFromSourceToCoequalizer
      6.10-6 MorphismFromSourceToCoequalizerWithGivenCoequalizer
      6.10-7 UniversalMorphismFromCoequalizer
      6.10-8 UniversalMorphismFromCoequalizerWithGivenCoequalizer
      6.10-9 CoequalizerFunctorial
      6.10-10 CoequalizerFunctorialWithGivenCoequalizers
    6.11 [33X[0;0YFiber Product[133X
      6.11-1 IsomorphismFromFiberProductToKernelOfDiagonalDifference
      6.11-2 IsomorphismFromKernelOfDiagonalDifferenceToFiberProduct
      6.11-3 IsomorphismFromFiberProductToEqualizerOfDirectProductDiagram
      6.11-4 IsomorphismFromEqualizerOfDirectProductDiagramToFiberProduct
      6.11-5 DirectSumDiagonalDifference
      6.11-6 FiberProductEmbeddingInDirectSum
      6.11-7 FiberProduct
      6.11-8 FiberProductOp
      6.11-9 ProjectionInFactorOfFiberProduct
      6.11-10 ProjectionInFactorOfFiberProductWithGivenFiberProduct
      6.11-11 MorphismFromFiberProductToSink
      6.11-12 MorphismFromFiberProductToSinkWithGivenFiberProduct
      6.11-13 UniversalMorphismIntoFiberProduct
      6.11-14 UniversalMorphismIntoFiberProductWithGivenFiberProduct
      6.11-15 FiberProductFunctorial
      6.11-16 FiberProductFunctorialWithGivenFiberProducts
    6.12 [33X[0;0YPushout[133X
      6.12-1 IsomorphismFromPushoutToCokernelOfDiagonalDifference
      6.12-2 IsomorphismFromCokernelOfDiagonalDifferenceToPushout
      6.12-3 IsomorphismFromPushoutToCoequalizerOfCoproductDiagram
      6.12-4 IsomorphismFromCoequalizerOfCoproductDiagramToPushout
      6.12-5 DirectSumCodiagonalDifference
      6.12-6 DirectSumProjectionInPushout
      6.12-7 Pushout
      6.12-8 Pushout
      6.12-9 InjectionOfCofactorOfPushout
      6.12-10 InjectionOfCofactorOfPushoutWithGivenPushout
      6.12-11 MorphismFromSourceToPushout
      6.12-12 MorphismFromSourceToPushoutWithGivenPushout
      6.12-13 UniversalMorphismFromPushout
      6.12-14 UniversalMorphismFromPushoutWithGivenPushout
      6.12-15 PushoutFunctorial
      6.12-16 PushoutFunctorialWithGivenPushouts
    6.13 [33X[0;0YImage[133X
      6.13-1 IsomorphismFromImageObjectToKernelOfCokernel
      6.13-2 IsomorphismFromKernelOfCokernelToImageObject
      6.13-3 ImageObject
      6.13-4 ImageEmbedding
      6.13-5 ImageEmbeddingWithGivenImageObject
      6.13-6 CoastrictionToImage
      6.13-7 CoastrictionToImageWithGivenImageObject
      6.13-8 UniversalMorphismFromImage
      6.13-9 UniversalMorphismFromImageWithGivenImageObject
      6.13-10 ImageObjectFunctorial
      6.13-11 ImageObjectFunctorialWithGivenImageObjects
    6.14 [33X[0;0YCoimage[133X
      6.14-1 MorphismFromCoimageToImage
      6.14-2 MorphismFromCoimageToImageWithGivenObjects
      6.14-3 InverseMorphismFromCoimageToImage
      6.14-4 InverseMorphismFromCoimageToImageWithGivenObjects
      6.14-5 IsomorphismFromCoimageToCokernelOfKernel
      6.14-6 IsomorphismFromCokernelOfKernelToCoimage
      6.14-7 CoimageObject
      6.14-8 CoimageProjection
      6.14-9 CoimageProjectionWithGivenCoimageObject
      6.14-10 AstrictionToCoimage
      6.14-11 AstrictionToCoimageWithGivenCoimageObject
      6.14-12 UniversalMorphismIntoCoimage
      6.14-13 UniversalMorphismIntoCoimageWithGivenCoimageObject
      6.14-14 CanonicalIdentificationFromImageObjectToCoimage
      6.14-15 CanonicalIdentificationFromCoimageToImageObject
      6.14-16 CoimageObjectFunctorial
      6.14-17 CoimageObjectFunctorialWithGivenCoimageObjects
    6.15 [33X[0;0YHomology objects[133X
      6.15-1 HomologyObject
      6.15-2 HomologyObjectFunctorial
      6.15-3 HomologyObjectFunctorialWithGivenHomologyObjects
      6.15-4 IsomorphismFromHomologyObjectToItsConstructionAsAnImageObject
      6.15-5 IsomorphismFromItsConstructionAsAnImageObjectToHomologyObject
    6.16 [33X[0;0YProjective covers and injective envelopes[133X
      6.16-1 ProjectiveCoverObject
      6.16-2 EpimorphismFromProjectiveCoverObject
      6.16-3 EpimorphismFromProjectiveCoverObjectWithGivenProjectiveCoverObject
      6.16-4 InjectiveEnvelopeObject
      6.16-5 MonomorphismIntoInjectiveEnvelopeObject
      6.16-6 MonomorphismIntoInjectiveEnvelopeObjectWithGivenInjectiveEnvelopeObject
  7 [33X[0;0YAdd Functions[133X
    7.1 [33X[0;0YFunctions Installed by Add[133X
    7.2 [33X[0;0YAdd Method[133X
    7.3 [33X[0;0YInstallAdd Function[133X
      7.3-1 CapInternalInstallAdd
    7.4 [33X[0;0YEnhancing the method name record[133X
    7.5 [33X[0;0YPrepare functions[133X
      7.5-1 CAPOperationPrepareFunction
      7.5-2 CAPAddPrepareFunction
      7.5-3 ListCAPPrepareFunctions
    7.6 [33X[0;0YAvailable Add functions[133X
      7.6-1 AddAdditionForMorphisms
      7.6-2 AddAdditiveGenerators
      7.6-3 AddAdditiveInverseForMorphisms
      7.6-4 AddAstrictionToCoimage
      7.6-5 AddAstrictionToCoimageWithGivenCoimageObject
      7.6-6 AddBasisOfExternalHom
      7.6-7 AddCanonicalIdentificationFromCoimageToImageObject
      7.6-8 AddCanonicalIdentificationFromImageObjectToCoimage
      7.6-9 AddCoastrictionToImage
      7.6-10 AddCoastrictionToImageWithGivenImageObject
      7.6-11 AddCoefficientsOfMorphism
      7.6-12 AddCoequalizer
      7.6-13 AddCoequalizerFunctorial
      7.6-14 AddCoequalizerFunctorialWithGivenCoequalizers
      7.6-15 AddCoimageObject
      7.6-16 AddCoimageObjectFunctorial
      7.6-17 AddCoimageObjectFunctorialWithGivenCoimageObjects
      7.6-18 AddCoimageProjection
      7.6-19 AddCoimageProjectionWithGivenCoimageObject
      7.6-20 AddCokernelColift
      7.6-21 AddCokernelColiftWithGivenCokernelObject
      7.6-22 AddCokernelObject
      7.6-23 AddCokernelObjectFunctorial
      7.6-24 AddCokernelObjectFunctorialWithGivenCokernelObjects
      7.6-25 AddCokernelProjection
      7.6-26 AddCokernelProjectionWithGivenCokernelObject
      7.6-27 AddColift
      7.6-28 AddColiftAlongEpimorphism
      7.6-29 AddColiftOrFail
      7.6-30 AddComponentOfMorphismFromDirectSum
      7.6-31 AddComponentOfMorphismIntoDirectSum
      7.6-32 AddCoproduct
      7.6-33 AddCoproductFunctorial
      7.6-34 AddCoproductFunctorialWithGivenCoproducts
      7.6-35 AddDirectProduct
      7.6-36 AddDirectProductFunctorial
      7.6-37 AddDirectProductFunctorialWithGivenDirectProducts
      7.6-38 AddDirectSum
      7.6-39 AddDirectSumCodiagonalDifference
      7.6-40 AddDirectSumDiagonalDifference
      7.6-41 AddDirectSumFunctorial
      7.6-42 AddDirectSumFunctorialWithGivenDirectSums
      7.6-43 AddDirectSumProjectionInPushout
      7.6-44 AddDistinguishedObjectOfHomomorphismStructure
      7.6-45 AddEmbeddingOfEqualizer
      7.6-46 AddEmbeddingOfEqualizerWithGivenEqualizer
      7.6-47 AddEpimorphismFromProjectiveCoverObject
      7.6-48 AddEpimorphismFromProjectiveCoverObjectWithGivenProjectiveCoverObject
      7.6-49 AddEpimorphismFromSomeProjectiveObject
      7.6-50 AddEpimorphismFromSomeProjectiveObjectWithGivenSomeProjectiveObject
      7.6-51 AddEqualizer
      7.6-52 AddEqualizerFunctorial
      7.6-53 AddEqualizerFunctorialWithGivenEqualizers
      7.6-54 AddFiberProduct
      7.6-55 AddFiberProductEmbeddingInDirectSum
      7.6-56 AddFiberProductFunctorial
      7.6-57 AddFiberProductFunctorialWithGivenFiberProducts
      7.6-58 AddHomologyObject
      7.6-59 AddHomologyObjectFunctorialWithGivenHomologyObjects
      7.6-60 AddHomomorphismStructureOnMorphisms
      7.6-61 AddHomomorphismStructureOnMorphismsWithGivenObjects
      7.6-62 AddHomomorphismStructureOnObjects
      7.6-63 AddHorizontalPostCompose
      7.6-64 AddHorizontalPreCompose
      7.6-65 AddIdentityMorphism
      7.6-66 AddIdentityTwoCell
      7.6-67 AddImageEmbedding
      7.6-68 AddImageEmbeddingWithGivenImageObject
      7.6-69 AddImageObject
      7.6-70 AddImageObjectFunctorial
      7.6-71 AddImageObjectFunctorialWithGivenImageObjects
      7.6-72 AddIndecomposableInjectiveObjects
      7.6-73 AddIndecomposableProjectiveObjects
      7.6-74 AddInitialObject
      7.6-75 AddInitialObjectFunctorial
      7.6-76 AddInitialObjectFunctorialWithGivenInitialObjects
      7.6-77 AddInjectionOfCofactorOfCoproduct
      7.6-78 AddInjectionOfCofactorOfCoproductWithGivenCoproduct
      7.6-79 AddInjectionOfCofactorOfDirectSum
      7.6-80 AddInjectionOfCofactorOfDirectSumWithGivenDirectSum
      7.6-81 AddInjectionOfCofactorOfPushout
      7.6-82 AddInjectionOfCofactorOfPushoutWithGivenPushout
      7.6-83 AddInjectiveColift
      7.6-84 AddInjectiveDimension
      7.6-85 AddInjectiveEnvelopeObject
      7.6-86 AddInterpretMorphismAsMorphismFromDistinguishedObjectToHomomorphismStructure
      7.6-87 AddInterpretMorphismAsMorphismFromDistinguishedObjectToHomomorphismStructureWithGivenObjects
      7.6-88 AddInterpretMorphismFromDistinguishedObjectToHomomorphismStructureAsMorphism
      7.6-89 AddInverseForMorphisms
      7.6-90 AddInverseMorphismFromCoimageToImageWithGivenObjects
      7.6-91 AddIsAutomorphism
      7.6-92 AddIsBijectiveObject
      7.6-93 AddIsCodominating
      7.6-94 AddIsColiftable
      7.6-95 AddIsColiftableAlongEpimorphism
      7.6-96 AddIsCongruentForMorphisms
      7.6-97 AddIsDominating
      7.6-98 AddIsEndomorphism
      7.6-99 AddIsEpimorphism
      7.6-100 AddIsEqualAsFactorobjects
      7.6-101 AddIsEqualAsSubobjects
      7.6-102 AddIsEqualForCacheForMorphisms
      7.6-103 AddIsEqualForCacheForObjects
      7.6-104 AddIsEqualForMorphisms
      7.6-105 AddIsEqualForMorphismsOnMor
      7.6-106 AddIsEqualForObjects
      7.6-107 AddIsEqualToIdentityMorphism
      7.6-108 AddIsEqualToZeroMorphism
      7.6-109 AddIsHomSetInhabited
      7.6-110 AddIsIdempotent
      7.6-111 AddIsInitial
      7.6-112 AddIsInjective
      7.6-113 AddIsIsomorphism
      7.6-114 AddIsLiftable
      7.6-115 AddIsLiftableAlongMonomorphism
      7.6-116 AddIsMonomorphism
      7.6-117 AddIsOne
      7.6-118 AddIsProjective
      7.6-119 AddIsSplitEpimorphism
      7.6-120 AddIsSplitMonomorphism
      7.6-121 AddIsTerminal
      7.6-122 AddIsWellDefinedForMorphisms
      7.6-123 AddIsWellDefinedForObjects
      7.6-124 AddIsWellDefinedForTwoCells
      7.6-125 AddIsZeroForMorphisms
      7.6-126 AddIsZeroForObjects
      7.6-127 AddIsomorphismFromCoequalizerOfCoproductDiagramToPushout
      7.6-128 AddIsomorphismFromCoimageToCokernelOfKernel
      7.6-129 AddIsomorphismFromCokernelOfDiagonalDifferenceToPushout
      7.6-130 AddIsomorphismFromCokernelOfKernelToCoimage
      7.6-131 AddIsomorphismFromCoproductToDirectSum
      7.6-132 AddIsomorphismFromDirectProductToDirectSum
      7.6-133 AddIsomorphismFromDirectSumToCoproduct
      7.6-134 AddIsomorphismFromDirectSumToDirectProduct
      7.6-135 AddIsomorphismFromEqualizerOfDirectProductDiagramToFiberProduct
      7.6-136 AddIsomorphismFromFiberProductToEqualizerOfDirectProductDiagram
      7.6-137 AddIsomorphismFromFiberProductToKernelOfDiagonalDifference
      7.6-138 AddIsomorphismFromHomologyObjectToItsConstructionAsAnImageObject
      7.6-139 AddIsomorphismFromImageObjectToKernelOfCokernel
      7.6-140 AddIsomorphismFromInitialObjectToZeroObject
      7.6-141 AddIsomorphismFromItsConstructionAsAnImageObjectToHomologyObject
      7.6-142 AddIsomorphismFromKernelOfCokernelToImageObject
      7.6-143 AddIsomorphismFromKernelOfDiagonalDifferenceToFiberProduct
      7.6-144 AddIsomorphismFromPushoutToCoequalizerOfCoproductDiagram
      7.6-145 AddIsomorphismFromPushoutToCokernelOfDiagonalDifference
      7.6-146 AddIsomorphismFromTerminalObjectToZeroObject
      7.6-147 AddIsomorphismFromZeroObjectToInitialObject
      7.6-148 AddIsomorphismFromZeroObjectToTerminalObject
      7.6-149 AddKernelEmbedding
      7.6-150 AddKernelEmbeddingWithGivenKernelObject
      7.6-151 AddKernelLift
      7.6-152 AddKernelLiftWithGivenKernelObject
      7.6-153 AddKernelObject
      7.6-154 AddKernelObjectFunctorial
      7.6-155 AddKernelObjectFunctorialWithGivenKernelObjects
      7.6-156 AddLift
      7.6-157 AddLiftAlongMonomorphism
      7.6-158 AddLiftOrFail
      7.6-159 AddMereExistenceOfSolutionOfLinearSystemInAbCategory
      7.6-160 AddMonomorphismIntoInjectiveEnvelopeObject
      7.6-161 AddMonomorphismIntoInjectiveEnvelopeObjectWithGivenInjectiveEnvelopeObject
      7.6-162 AddMonomorphismIntoSomeInjectiveObject
      7.6-163 AddMonomorphismIntoSomeInjectiveObjectWithGivenSomeInjectiveObject
      7.6-164 AddMorphismBetweenDirectSums
      7.6-165 AddMorphismBetweenDirectSumsWithGivenDirectSums
      7.6-166 AddMorphismConstructor
      7.6-167 AddMorphismDatum
      7.6-168 AddMorphismFromCoimageToImageWithGivenObjects
      7.6-169 AddMorphismFromEqualizerToSink
      7.6-170 AddMorphismFromEqualizerToSinkWithGivenEqualizer
      7.6-171 AddMorphismFromFiberProductToSink
      7.6-172 AddMorphismFromFiberProductToSinkWithGivenFiberProduct
      7.6-173 AddMorphismFromKernelObjectToSink
      7.6-174 AddMorphismFromKernelObjectToSinkWithGivenKernelObject
      7.6-175 AddMorphismFromSourceToCoequalizer
      7.6-176 AddMorphismFromSourceToCoequalizerWithGivenCoequalizer
      7.6-177 AddMorphismFromSourceToCokernelObject
      7.6-178 AddMorphismFromSourceToCokernelObjectWithGivenCokernelObject
      7.6-179 AddMorphismFromSourceToPushout
      7.6-180 AddMorphismFromSourceToPushoutWithGivenPushout
      7.6-181 AddMultiplyWithElementOfCommutativeRingForMorphisms
      7.6-182 AddObjectConstructor
      7.6-183 AddObjectDatum
      7.6-184 AddPostCompose
      7.6-185 AddPostComposeList
      7.6-186 AddPostInverseForMorphisms
      7.6-187 AddPreCompose
      7.6-188 AddPreComposeList
      7.6-189 AddPreInverseForMorphisms
      7.6-190 AddProjectionInFactorOfDirectProduct
      7.6-191 AddProjectionInFactorOfDirectProductWithGivenDirectProduct
      7.6-192 AddProjectionInFactorOfDirectSum
      7.6-193 AddProjectionInFactorOfDirectSumWithGivenDirectSum
      7.6-194 AddProjectionInFactorOfFiberProduct
      7.6-195 AddProjectionInFactorOfFiberProductWithGivenFiberProduct
      7.6-196 AddProjectionOntoCoequalizer
      7.6-197 AddProjectionOntoCoequalizerWithGivenCoequalizer
      7.6-198 AddProjectiveCoverObject
      7.6-199 AddProjectiveDimension
      7.6-200 AddProjectiveLift
      7.6-201 AddPushout
      7.6-202 AddPushoutFunctorial
      7.6-203 AddPushoutFunctorialWithGivenPushouts
      7.6-204 AddRandomMorphismByInteger
      7.6-205 AddRandomMorphismByList
      7.6-206 AddRandomMorphismWithFixedRangeByInteger
      7.6-207 AddRandomMorphismWithFixedRangeByList
      7.6-208 AddRandomMorphismWithFixedSourceAndRangeByInteger
      7.6-209 AddRandomMorphismWithFixedSourceAndRangeByList
      7.6-210 AddRandomMorphismWithFixedSourceByInteger
      7.6-211 AddRandomMorphismWithFixedSourceByList
      7.6-212 AddRandomObjectByInteger
      7.6-213 AddRandomObjectByList
      7.6-214 AddSimplifyEndo
      7.6-215 AddSimplifyEndo_IsoFromInputObject
      7.6-216 AddSimplifyEndo_IsoToInputObject
      7.6-217 AddSimplifyMorphism
      7.6-218 AddSimplifyObject
      7.6-219 AddSimplifyObject_IsoFromInputObject
      7.6-220 AddSimplifyObject_IsoToInputObject
      7.6-221 AddSimplifyRange
      7.6-222 AddSimplifyRange_IsoFromInputObject
      7.6-223 AddSimplifyRange_IsoToInputObject
      7.6-224 AddSimplifySource
      7.6-225 AddSimplifySourceAndRange
      7.6-226 AddSimplifySourceAndRange_IsoFromInputRange
      7.6-227 AddSimplifySourceAndRange_IsoFromInputSource
      7.6-228 AddSimplifySourceAndRange_IsoToInputRange
      7.6-229 AddSimplifySourceAndRange_IsoToInputSource
      7.6-230 AddSimplifySource_IsoFromInputObject
      7.6-231 AddSimplifySource_IsoToInputObject
      7.6-232 AddSolveLinearSystemInAbCategory
      7.6-233 AddSolveLinearSystemInAbCategoryOrFail
      7.6-234 AddSomeInjectiveObject
      7.6-235 AddSomeProjectiveObject
      7.6-236 AddSomeReductionBySplitEpiSummand
      7.6-237 AddSomeReductionBySplitEpiSummand_MorphismFromInputRange
      7.6-238 AddSomeReductionBySplitEpiSummand_MorphismToInputRange
      7.6-239 AddSubtractionForMorphisms
      7.6-240 AddSumOfMorphisms
      7.6-241 AddTerminalObject
      7.6-242 AddTerminalObjectFunctorial
      7.6-243 AddTerminalObjectFunctorialWithGivenTerminalObjects
      7.6-244 AddUniversalMorphismFromCoequalizer
      7.6-245 AddUniversalMorphismFromCoequalizerWithGivenCoequalizer
      7.6-246 AddUniversalMorphismFromCoproduct
      7.6-247 AddUniversalMorphismFromCoproductWithGivenCoproduct
      7.6-248 AddUniversalMorphismFromDirectSum
      7.6-249 AddUniversalMorphismFromDirectSumWithGivenDirectSum
      7.6-250 AddUniversalMorphismFromImage
      7.6-251 AddUniversalMorphismFromImageWithGivenImageObject
      7.6-252 AddUniversalMorphismFromInitialObject
      7.6-253 AddUniversalMorphismFromInitialObjectWithGivenInitialObject
      7.6-254 AddUniversalMorphismFromPushout
      7.6-255 AddUniversalMorphismFromPushoutWithGivenPushout
      7.6-256 AddUniversalMorphismFromZeroObject
      7.6-257 AddUniversalMorphismFromZeroObjectWithGivenZeroObject
      7.6-258 AddUniversalMorphismIntoCoimage
      7.6-259 AddUniversalMorphismIntoCoimageWithGivenCoimageObject
      7.6-260 AddUniversalMorphismIntoDirectProduct
      7.6-261 AddUniversalMorphismIntoDirectProductWithGivenDirectProduct
      7.6-262 AddUniversalMorphismIntoDirectSum
      7.6-263 AddUniversalMorphismIntoDirectSumWithGivenDirectSum
      7.6-264 AddUniversalMorphismIntoEqualizer
      7.6-265 AddUniversalMorphismIntoEqualizerWithGivenEqualizer
      7.6-266 AddUniversalMorphismIntoFiberProduct
      7.6-267 AddUniversalMorphismIntoFiberProductWithGivenFiberProduct
      7.6-268 AddUniversalMorphismIntoTerminalObject
      7.6-269 AddUniversalMorphismIntoTerminalObjectWithGivenTerminalObject
      7.6-270 AddUniversalMorphismIntoZeroObject
      7.6-271 AddUniversalMorphismIntoZeroObjectWithGivenZeroObject
      7.6-272 AddVerticalPostCompose
      7.6-273 AddVerticalPreCompose
      7.6-274 AddZeroMorphism
      7.6-275 AddZeroObject
      7.6-276 AddZeroObjectFunctorial
      7.6-277 AddZeroObjectFunctorialWithGivenZeroObjects
  8 [33X[0;0YManaging Derived Methods[133X
    8.1 [33X[0;0YInfo Class[133X
      8.1-1 DerivationInfo
      8.1-2 ActivateDerivationInfo
      8.1-3 DeactivateDerivationInfo
    8.2 [33X[0;0YDerivation Objects[133X
      8.2-1 IsDerivedMethod
      8.2-2 MakeDerivation
      8.2-3 DerivationName
      8.2-4 DerivationWeight
      8.2-5 DerivationFunction
      8.2-6 CategoryFilter
      8.2-7 IsApplicableToCategory
      8.2-8 TargetOperation
      8.2-9 UsedOperationsWithMultiplesAndCategoryGetters
      8.2-10 InstallDerivationForCategory
      8.2-11 FunctionCalledBeforeInstallation
    8.3 [33X[0;0YDerivation Graphs[133X
      8.3-1 IsDerivedMethodGraph
      8.3-2 MakeDerivationGraph
      8.3-3 AddOperationsToDerivationGraph
      8.3-4 AddDerivation
      8.3-5 AddDerivation
      8.3-6 AddDerivation
      8.3-7 AddDerivation
      8.3-8 AddDerivationToCAP
      8.3-9 AddWithGivenDerivationPairToCAP
      8.3-10 Operations
      8.3-11 DerivationsUsingOperation
      8.3-12 DerivationsOfOperation
    8.4 [33X[0;0YManaging Derivations in a Category[133X
      8.4-1 IsOperationWeightList
      8.4-2 MakeOperationWeightList
      8.4-3 DerivationGraph
      8.4-4 CategoryOfOperationWeightList
      8.4-5 CurrentOperationWeight
      8.4-6 OperationWeightUsingDerivation
      8.4-7 DerivationOfOperation
      8.4-8 InstallDerivationsUsingOperation
      8.4-9 Reevaluate
      8.4-10 Saturate
      8.4-11 AddPrimitiveOperation
      8.4-12 PrintDerivationTree
      8.4-13 PrintTree
      8.4-14 PrintTreeRec
    8.5 [33X[0;0YMin Heaps for Strings[133X
      8.5-1 IsStringMinHeap
      8.5-2 StringMinHeap
      8.5-3 Add
      8.5-4 ExtractMin
      8.5-5 DecreaseKey
      8.5-6 IsEmptyHeap
      8.5-7 HeapSize
      8.5-8 Contains
      8.5-9 Swap
      8.5-10 Heapify
  9 [33X[0;0YTechnical Details[133X
    9.1 [33X[0;0YThe Category Cat[133X
      9.1-1 ObjectCache
      9.1-2 MorphismCache
    9.2 [33X[0;0YTools[133X
      9.2-1 DeclareFamilyProperty
      9.2-2 CAP_INTERNAL_REPLACE_STRING_WITH_FILTER
      9.2-3 CAP_INTERNAL_REPLACE_STRINGS_WITH_FILTERS
      9.2-4 CAP_INTERNAL_MERGE_FILTER_LISTS
      9.2-5 CAP_INTERNAL_RETURN_OPTION_OR_DEFAULT
      9.2-6 CAP_INTERNAL_FIND_APPEARANCE_OF_SYMBOL_IN_FUNCTION
      9.2-7 CAP_INTERNAL_MERGE_PRECONDITIONS_LIST
      9.2-8 CAP_INTERNAL_ASSERT_IS_CELL_OF_CATEGORY
      9.2-9 CAP_INTERNAL_ASSERT_IS_OBJECT_OF_CATEGORY
      9.2-10 CAP_INTERNAL_ASSERT_IS_MORPHISM_OF_CATEGORY
      9.2-11 CAP_INTERNAL_ASSERT_IS_TWO_CELL_OF_CATEGORY
      9.2-12 CAP_INTERNAL_ASSERT_IS_LIST_OF_OBJECTS_OF_CATEGORY
      9.2-13 CAP_INTERNAL_ASSERT_IS_LIST_OF_MORPHISMS_OF_CATEGORY
      9.2-14 CAP_INTERNAL_ASSERT_IS_LIST_OF_TWO_CELLS_OF_CATEGORY
      9.2-15 CAP_INTERNAL_ASSERT_IS_NON_NEGATIVE_INTEGER_OR_INFINITY
      9.2-16 CachingStatistic
      9.2-17 BrowseCachingStatistic
      9.2-18 InstallDeprecatedAlias
      9.2-19 IsSpecializationOfFilter
      9.2-20 IsSpecializationOfFilterList
      9.2-21 InstallMethodForCompilerForCAP
      9.2-22 InstallOtherMethodForCompilerForCAP
      9.2-23 CapJitAddKnownMethod
      9.2-24 CapJitAddTypeSignature
      9.2-25 CapJitAddTypeSignatureDeferred
      9.2-26 CapJitDataTypeOfCategory
      9.2-27 CapFixpoint
      9.2-28 Iterated
      9.2-29 TransitivelyNeededOtherPackages
      9.2-30 PackageOfCAPOperation
      9.2-31 SafePosition
      9.2-32 SafeUniquePosition
      9.2-33 SafePositionProperty
      9.2-34 SafeUniquePositionProperty
      9.2-35 SafeFirst
      9.2-36 SafeUniqueEntry
      9.2-37 NTuple
      9.2-38 Pair
      9.2-39 Triple
      9.2-40 HandlePrecompiledTowers
      9.2-41 CAP_JIT_INCOMPLETE_LOGIC
      9.2-42 ListWithKeys
      9.2-43 SumWithKeys
      9.2-44 ProductWithKeys
      9.2-45 ForAllWithKeys
      9.2-46 ForAnyWithKeys
      9.2-47 NumberWithKeys
      9.2-48 FilteredWithKeys
      9.2-49 FirstWithKeys
      9.2-50 LastWithKeys
  10 [33X[0;0YLimits and Colimits[133X
    10.1 [33X[0;0YSpecification of Limits and Colimits[133X
    10.2 [33X[0;0YEnhancing Limit Specifications[133X
    10.3 [33X[0;0YFunctions[133X
      10.3-1 CAP_INTERNAL_GENERATE_CONVENIENCE_METHODS_FOR_LIMITS
      10.3-2 CAP_INTERNAL_VALIDATE_LIMITS_IN_NAME_RECORD
  11 [33X[0;0YThe Category Constructor[133X
    11.1 [33X[0;0YInfo class[133X
      11.1-1 InfoCategoryConstructor
    11.2 [33X[0;0YConstructors[133X
      11.2-1 CategoryConstructor
  12 [33X[0;0YCreate wrapper hulls of a category[133X
    12.1 [33X[0;0YGAP categories[133X
      12.1-1 IsWrapperCapCategory
      12.1-2 IsWrapperCapCategoryObject
      12.1-3 IsWrapperCapCategoryMorphism
    12.2 [33X[0;0YAttributes[133X
      12.2-1 ModelingCategory
      12.2-2 UnderlyingCell
      12.2-3 UnderlyingCell
    12.3 [33X[0;0YConstructors[133X
      12.3-1 AsObjectInWrapperCategory
      12.3-2 AsMorphismInWrapperCategory
      12.3-3 AsMorphismInWrapperCategory
      12.3-4 /
      12.3-5 WrapperCategory
      12.3-6 WrappingFunctor
      12.3-7 ModelingObject
      12.3-8 ModeledObject
      12.3-9 ModelingMorphism
      12.3-10 ModeledMorphism
  13 [33X[0;0YDummy categories[133X
    13.1 [33X[0;0YGAP categories[133X
      13.1-1 IsDummyCategory
      13.1-2 IsDummyCategoryObject
      13.1-3 IsDummyCategoryMorphism
    13.2 [33X[0;0YConstructors[133X
      13.2-1 DummyCategory
  14 [33X[0;0YExamples and Tests[133X
    14.1 [33X[0;0YDummy category[133X
    14.2 [33X[0;0YFunctors[133X
    14.3 [33X[0;0YHandlePrecompiledTowers[133X
    14.4 [33X[0;0YHomomorphism structure[133X
    14.5 [33X[0;0YHomology object[133X
    14.6 [33X[0;0YLiftable[133X
    14.7 [33X[0;0YWrapperCategory[133X
    14.8 [33X[0;0YMonoidal Categories[133X
    14.9 [33X[0;0YMorphismFromSourceToPushout and MorphismFromFiberProductToSink[133X
    14.10 [33X[0;0YOpposite category[133X
    14.11 [33X[0;0YTerminal category[133X
    14.12 [33X[0;0YGeneralized Morphisms Category[133X
    14.13 [33X[0;0YIsWellDefined[133X
    14.14 [33X[0;0YKernel[133X
    14.15 [33X[0;0YFiberProduct[133X
  15 [33X[0;0YTerminal category[133X
    15.1 [33X[0;0Y[5XGAP[105X Categories[133X
      15.1-1 IsCapTerminalCategoryWithSingleObject
      15.1-2 IsObjectInCapTerminalCategoryWithSingleObject
      15.1-3 IsMorphismInCapTerminalCategoryWithSingleObject
      15.1-4 IsCapTerminalCategoryWithMultipleObjects
      15.1-5 IsObjectInCapTerminalCategoryWithMultipleObjects
      15.1-6 IsMorphismInCapTerminalCategoryWithMultipleObjects
      15.1-7 IsTerminalCategory
    15.2 [33X[0;0YConstructors[133X
      15.2-1 TerminalCategoryWithSingleObject
      15.2-2 TerminalCategoryWithMultipleObjects
      15.2-3 CAP_INTERNAL_CONSTRUCTOR_FOR_TERMINAL_CATEGORY
    15.3 [33X[0;0YAttributes[133X
      15.3-1 UniqueObject
      15.3-2 UniqueMorphism
      15.3-3 FunctorFromTerminalCategory
  
  
  [32X
