  
  
                          [1X GeneralizedMorphismsForCAP [101X
  
  
         [1X Implementations of generalized morphisms for the CAP project [101X
  
  
                                   2022.12-01
  
  
                                14 December 2022
  
  
                               Sebastian Gutsche
  
                                Sebastian Posur
  
  
  
  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
  
  
  
  -------------------------------------------------------
  
  
  [1XContents (GeneralizedMorphismsForCAP)[101X
  
  1 [33X[0;0YGeneralized Morphism Category[133X
    1.1 [33X[0;0YGAP Categories[133X
      1.1-1 IsGeneralizedMorphismCategoryObject
      1.1-2 IsGeneralizedMorphism
    1.2 [33X[0;0YAttributes[133X
      1.2-1 UnderlyingHonestObject
      1.2-2 DomainEmbedding
      1.2-3 GeneralizedImageEmbedding
      1.2-4 DefectEmbedding
      1.2-5 GeneralizedKernelEmbedding
      1.2-6 CodomainProjection
      1.2-7 GeneralizedCokernelProjection
      1.2-8 CodefectProjection
      1.2-9 GeneralizedCoimageProjection
      1.2-10 AssociatedMorphism
      1.2-11 DomainAssociatedMorphismCodomainTriple
      1.2-12 HonestRepresentative
      1.2-13 GeneralizedInverse
      1.2-14 IdempotentDefinedBySubobject
      1.2-15 IdempotentDefinedByFactorobject
      1.2-16 UnderlyingHonestCategory
    1.3 [33X[0;0YOperations[133X
      1.3-1 GeneralizedMorphismFromFactorToSubobject
      1.3-2 CommonRestriction
      1.3-3 ConcatenationProduct
    1.4 [33X[0;0YProperties[133X
      1.4-1 IsHonest
      1.4-2 HasFullDomain
      1.4-3 HasFullCodomain
      1.4-4 IsSingleValued
      1.4-5 IsTotal
    1.5 [33X[0;0YConvenience methods[133X
      1.5-1 GeneralizedMorphismCategory
      1.5-2 GeneralizedMorphismObject
      1.5-3 AsGeneralizedMorphism
      1.5-4 GeneralizedMorphism
      1.5-5 GeneralizedMorphism
      1.5-6 GeneralizedMorphismWithRangeAid
      1.5-7 GeneralizedMorphismWithSourceAid
  2 [33X[0;0YGeneralized Morphism Category by Cospans[133X
    2.1 [33X[0;0YGAP Categories[133X
      2.1-1 IsGeneralizedMorphismCategoryByCospansObject
      2.1-2 IsGeneralizedMorphismByCospan
    2.2 [33X[0;0YProperties[133X
      2.2-1 HasIdentityAsReversedArrow
    2.3 [33X[0;0YAttributes[133X
      2.3-1 UnderlyingHonestObject
      2.3-2 Arrow
      2.3-3 ReversedArrow
      2.3-4 NormalizedCospanTuple
      2.3-5 PseudoInverse
      2.3-6 GeneralizedInverseByCospan
      2.3-7 IdempotentDefinedBySubobjectByCospan
      2.3-8 IdempotentDefinedByFactorobjectByCospan
      2.3-9 NormalizedCospan
    2.4 [33X[0;0YOperations[133X
      2.4-1 GeneralizedMorphismFromFactorToSubobjectByCospan
    2.5 [33X[0;0YConstructors[133X
      2.5-1 GeneralizedMorphismByCospan
      2.5-2 GeneralizedMorphismByCospan
      2.5-3 GeneralizedMorphismByCospanWithSourceAid
      2.5-4 AsGeneralizedMorphismByCospan
      2.5-5 GeneralizedMorphismCategoryByCospans
      2.5-6 GeneralizedMorphismByCospansObject
    2.6 [33X[0;0YConstructors of lifts of exact functors and natrual (iso)morphisms[133X
      2.6-1 AsGeneralizedMorphismByCospan
  3 [33X[0;0YGeneralized Morphism Category by Spans[133X
    3.1 [33X[0;0YGAP Categories[133X
      3.1-1 IsGeneralizedMorphismCategoryBySpansObject
      3.1-2 IsGeneralizedMorphismBySpan
    3.2 [33X[0;0YProperties[133X
      3.2-1 HasIdentityAsReversedArrow
    3.3 [33X[0;0YAttributes[133X
      3.3-1 UnderlyingHonestObject
      3.3-2 Arrow
      3.3-3 ReversedArrow
      3.3-4 NormalizedSpanTuple
      3.3-5 PseudoInverse
      3.3-6 GeneralizedInverseBySpan
      3.3-7 IdempotentDefinedBySubobjectBySpan
      3.3-8 IdempotentDefinedByFactorobjectBySpan
      3.3-9 NormalizedSpan
    3.4 [33X[0;0YOperations[133X
      3.4-1 GeneralizedMorphismFromFactorToSubobjectBySpan
    3.5 [33X[0;0YConstructors[133X
      3.5-1 GeneralizedMorphismBySpan
      3.5-2 GeneralizedMorphismBySpan
      3.5-3 GeneralizedMorphismBySpanWithRangeAid
      3.5-4 AsGeneralizedMorphismBySpan
      3.5-5 GeneralizedMorphismCategoryBySpans
      3.5-6 GeneralizedMorphismBySpansObject
  4 [33X[0;0YGeneralized Morphism Category by Three Arrows[133X
    4.1 [33X[0;0YGAP Categories[133X
      4.1-1 IsGeneralizedMorphismCategoryByThreeArrowsObject
      4.1-2 IsGeneralizedMorphismByThreeArrows
    4.2 [33X[0;0YProperties[133X
      4.2-1 HasIdentitiesAsReversedArrows
      4.2-2 HasIdentityAsSourceAid
      4.2-3 HasIdentityAsRangeAid
    4.3 [33X[0;0YAttributes[133X
      4.3-1 UnderlyingHonestObject
      4.3-2 SourceAid
      4.3-3 RangeAid
      4.3-4 Arrow
      4.3-5 PseudoInverse
      4.3-6 GeneralizedInverseByThreeArrows
      4.3-7 IdempotentDefinedBySubobjectByThreeArrows
      4.3-8 IdempotentDefinedByFactorobjectByThreeArrows
    4.4 [33X[0;0YOperations[133X
      4.4-1 GeneralizedMorphismFromFactorToSubobjectByThreeArrows
      4.4-2 CommonCoastriction
    4.5 [33X[0;0YConstructors[133X
      4.5-1 GeneralizedMorphismByThreeArrows
      4.5-2 GeneralizedMorphismByThreeArrowsWithSourceAid
      4.5-3 GeneralizedMorphismByThreeArrowsWithRangeAid
      4.5-4 AsGeneralizedMorphismByThreeArrows
      4.5-5 GeneralizedMorphismCategoryByThreeArrows
      4.5-6 GeneralizedMorphismByThreeArrowsObject
  5 [33X[0;0YConversion functors for generalized morphisms[133X
    5.1 [33X[0;0YFunctors from Cospans[133X
      5.1-1 FunctorFromCospansToThreeArrows
      5.1-2 FunctorFromCospansToSpans
    5.2 [33X[0;0YFunctors from Spans[133X
      5.2-1 FunctorFromSpansToThreeArrows
      5.2-2 FunctorFromSpansToCospans
    5.3 [33X[0;0YFunctors from Three Arrows[133X
      5.3-1 FunctorFromThreeArrowsToCospans
      5.3-2 FunctorFromThreeArrowsToSpans
  6 [33X[0;0YSerre Quotients Subcategory[133X
    6.1 [33X[0;0Yimplementation[133X
      6.1-1 FullSubcategoryByMembershipFunction
  7 [33X[0;0YSerre Quotients[133X
    7.1 [33X[0;0YGeneral operations[133X
      7.1-1 IsSerreQuotientCategoryObject
      7.1-2 IsSerreQuotientCategoryMorphism
      7.1-3 SerreQuotientCategory
      7.1-4 AsSerreQuotientCategoryObject
      7.1-5 SerreQuotientCategoryMorphism
      7.1-6 SerreQuotientCategoryMorphism
      7.1-7 SerreQuotientCategoryMorphism
      7.1-8 SerreQuotientCategoryMorphismWithSourceAid
      7.1-9 SerreQuotientCategoryMorphismWithRangeAid
      7.1-10 AsSerreQuotientCategoryMorphism
      7.1-11 SubcategoryMembershipTestFunctionForSerreQuotient
      7.1-12 UnderlyingHonestCategory
      7.1-13 UnderlyingGeneralizedMorphismCategory
      7.1-14 UnderlyingGeneralizedObject
      7.1-15 UnderlyingHonestObject
      7.1-16 UnderlyingGeneralizedMorphism
      7.1-17 CanonicalProjection
    7.2 [33X[0;0YSerre quotients by cospans[133X
      7.2-1 SerreQuotientCategoryByCospans
      7.2-2 AsSerreQuotientCategoryByCospansObject
      7.2-3 SerreQuotientCategoryByCospansMorphism
      7.2-4 SerreQuotientCategoryByCospansMorphism
      7.2-5 SerreQuotientCategoryByCospansMorphismWithSourceAid
      7.2-6 SerreQuotientCategoryByCospansMorphism
      7.2-7 AsSerreQuotientCategoryByCospansMorphism
    7.3 [33X[0;0YSerre Quotients by Spans[133X
      7.3-1 SerreQuotientCategoryBySpans
      7.3-2 AsSerreQuotientCategoryBySpansObject
      7.3-3 SerreQuotientCategoryBySpansMorphism
      7.3-4 SerreQuotientCategoryBySpansMorphism
      7.3-5 SerreQuotientCategoryBySpansMorphism
      7.3-6 SerreQuotientCategoryBySpansMorphismWithRangeAid
      7.3-7 AsSerreQuotientCategoryBySpansMorphism
    7.4 [33X[0;0YSerre Quotients modeled by three arrows[133X
      7.4-1 SerreQuotientCategoryByThreeArrows
      7.4-2 AsSerreQuotientCategoryByThreeArrowsObject
      7.4-3 SerreQuotientCategoryByThreeArrowsMorphism
      7.4-4 SerreQuotientCategoryByThreeArrowsMorphism
      7.4-5 SerreQuotientCategoryByThreeArrowsMorphismWithSourceAid
      7.4-6 SerreQuotientCategoryByThreeArrowsMorphismWithRangeAid
      7.4-7 AsSerreQuotientCategoryByThreeArrowsMorphism
  8 [33X[0;0YSerre Quotients Functors[133X
    8.1 [33X[0;0YFunctors[133X
      8.1-1 SerreQuotientConversionFunctor
  9 [33X[0;0YExamples and Tests[133X
    9.1 [33X[0;0YBasic Commands[133X
    9.2 [33X[0;0YIntersection of Nodal Curve and Cusp[133X
    9.3 [33X[0;0YSweep[133X
  
  
  [32X
