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CAP

Categories, Algorithms, Programming

2022.12-11

16 December 2022

Sebastian Gutsche
Email: gutsche@mathematik.uni-siegen.de
Homepage: https://sebasguts.github.io/
Address:
Department Mathematik
Universität Siegen
Walter-Flex-Straße 3
57068 Siegen
Germany

Sebastian Posur
Email: sebastian.posur@uni-siegen.de
Homepage: https://sebastianpos.github.io
Address:
Department Mathematik
Universität Siegen
Walter-Flex-Straße 3
57068 Siegen
Germany

Øystein Skartsæterhagen
Email: oysteini@math.ntnu.no
Homepage: http://www.math.ntnu.no/~oysteini/
Address:
NTNU
Institutt for matematiske fag
7491 Trondheim
Norway

Contents

1 CAP Categories
 1.1 Categories

  1.1-1 IsCapCategory
  1.1-2 IsCapCategoryCell
  1.1-3 IsCapCategoryObject
  1.1-4 IsCapCategoryMorphism
  1.1-5 IsCapCategoryTwoCell
 1.2 Categorical properties

  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 Constructor

  1.3-1 CreateCapCategory
  1.3-2 CreateCapCategory
  1.3-3 CreateCapCategory
  1.3-4 CreateCapCategoryWithDataTypes
 1.4 Internal Attributes

  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 Logic switcher

  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 Tool functions

  1.6-1 CanCompute
  1.6-2 CheckConstructivenessOfCategory
 1.7 Well-Definedness of Cells

  1.7-1 IsWellDefined
 1.8 Unpacking data structures

  1.8-1 Down
  1.8-2 DownOnlyMorphismData
  1.8-3 DownToBottom
 1.9 Caching

  1.9-1 SetCachingOfCategory
  1.9-2 SetCachingOfCategoryWeak
  1.9-3 SetDefaultCaching
 1.10 Sanity checks

  1.10-1 DisableInputSanityChecks
 1.11 Timing statistics

  1.11-1 EnableTimingStatistics
 1.12 Enable automatic calls of Add

  1.12-1 EnableAddForCategoricalOperations
 1.13 Performance tweaks
 1.14 LaTeX

  1.14-1 LaTeXOutput
  1.14-2 LaTeXOutput
2 Objects
 2.1 Attributes for the Type of Objects

  2.1-1 CapCategory
 2.2 Equality for Objects

  2.2-1 IsEqualForObjects
 2.3 Categorical Properties of Objects

  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 Random Objects

  2.4-1 RandomObjectByInteger
  2.4-2 RandomObjectByList
  2.4-3 RandomObject
  2.4-4 RandomObject
 2.5 Tool functions for caches

  2.5-1 IsEqualForCacheForObjects
 2.6 Adding Objects to a Category

  2.6-1 Add
  2.6-2 AddObject
  2.6-3 AddObjectRepresentation
  2.6-4 ObjectifyObjectForCAPWithAttributes
  2.6-5 CreateCapCategoryObjectWithAttributes
 2.7 Object constructors

  2.7-1 ObjectConstructor
  2.7-2 /
  2.7-3 ObjectDatum
 2.8 Well-Definedness of Objects

  2.8-1 IsWellDefinedForObjects
 2.9 Projectives

  2.9-1 SomeProjectiveObject
  2.9-2 EpimorphismFromSomeProjectiveObject
  2.9-3 EpimorphismFromSomeProjectiveObjectWithGivenSomeProjectiveObject
  2.9-4 ProjectiveLift
 2.10 Injectives

  2.10-1 SomeInjectiveObject
  2.10-2 MonomorphismIntoSomeInjectiveObject
  2.10-3 MonomorphismIntoSomeInjectiveObjectWithGivenSomeInjectiveObject
  2.10-4 InjectiveColift
 2.11 Simplified Objects

  2.11-1 Simplify
  2.11-2 SimplifyObject
  2.11-3 SimplifyObject_IsoFromInputObject
  2.11-4 SimplifyObject_IsoToInputObject
 2.12 Dimensions

  2.12-1 ProjectiveDimension
  2.12-2 InjectiveDimension
3 Morphisms
 3.1 Attributes for the Type of Morphisms

  3.1-1 CapCategory
  3.1-2 Source
  3.1-3 Range
 3.2 Morphism constructors

  3.2-1 MorphismConstructor
  3.2-2 MorphismDatum
 3.3 Categorical Properties of Morphisms

  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 Random Morphisms

  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 Non-Categorical Properties of Morphisms

  3.5-1 IsEqualToIdentityMorphism
  3.5-2 IsEqualToZeroMorphism
  3.5-3 IsEndomorphism
  3.5-4 IsAutomorphism
 3.6 Adding Morphisms to a Category

  3.6-1 Add
  3.6-2 AddMorphism
  3.6-3 AddMorphismRepresentation
  3.6-4 ObjectifyMorphismWithSourceAndRangeForCAPWithAttributes
  3.6-5 CreateCapCategoryMorphismWithAttributes
 3.7 Equality and Congruence for Morphisms

  3.7-1 IsCongruentForMorphisms
  3.7-2 IsEqualForMorphisms
  3.7-3 IsEqualForMorphismsOnMor
 3.8 Basic Operations for Morphisms in Ab-Categories

  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 Subobject and Factorobject Operations

  3.9-1 IsEqualAsSubobjects
  3.9-2 IsEqualAsFactorobjects
  3.9-3 IsDominating
  3.9-4 IsCodominating
 3.10 Identity Morphism and Composition of Morphisms

  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 Well-Definedness of Morphisms

  3.11-1 IsWellDefinedForMorphisms
 3.12 Lift/Colift

  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 Inverses

  3.13-1 InverseForMorphisms
  3.13-2 PreInverseForMorphisms
  3.13-3 PostInverseForMorphisms
 3.14 Tool functions for caches

  3.14-1 IsEqualForCacheForMorphisms
 3.15 IsHomSetInhabited

  3.15-1 IsHomSetInhabited
 3.16 Homomorphism structures

  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 Simplified Morphisms

  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 Reduction by split epi summands

  3.18-1 SomeReductionBySplitEpiSummand
  3.18-2 SomeReductionBySplitEpiSummand_MorphismToInputRange
  3.18-3 SomeReductionBySplitEpiSummand_MorphismFromInputRange
4 Category 2-Cells
 4.1 Attributes for the Type of 2-Cells

  4.1-1 Source
  4.1-2 Range
 4.2 Identity 2-Cell and Composition of 2-Cells

  4.2-1 IdentityTwoCell
  4.2-2 HorizontalPreCompose
  4.2-3 HorizontalPostCompose
  4.2-4 VerticalPreCompose
  4.2-5 VerticalPostCompose
 4.3 Well-Definedness for 2-Cells

  4.3-1 IsWellDefinedForTwoCells
5 Category of Categories
 5.1 The Category Cat

  5.1-1 CapCat
 5.2 Categories

  5.2-1 IsCapCategoryAsCatObject
  5.2-2 IsCapFunctor
  5.2-3 IsCapNaturalTransformation
 5.3 Constructors

  5.3-1 AsCatObject
  5.3-2 AsCapCategory
 5.4 Functors

  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 Natural transformations

  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 Universal Objects
 6.1 Kernel

  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 Cokernel

  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 Zero Object

  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 Terminal Object

  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 Initial Object

  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 Direct Sum

  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 Coproduct

  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 Direct Product

  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 Equalizer

  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 Coequalizer

  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 Fiber Product

  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 Pushout

  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 Image

  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 Coimage

  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 Homology objects

  6.15-1 HomologyObject
  6.15-2 HomologyObjectFunctorial
  6.15-3 HomologyObjectFunctorialWithGivenHomologyObjects
  6.15-4 IsomorphismFromHomologyObjectToItsConstructionAsAnImageObject
  6.15-5 IsomorphismFromItsConstructionAsAnImageObjectToHomologyObject
 6.16 Projective covers and injective envelopes

  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 Add Functions
 7.1 Functions Installed by Add
 7.2 Add Method
 7.3 InstallAdd Function

  7.3-1 CapInternalInstallAdd
 7.4 Enhancing the method name record
 7.5 Prepare functions

  7.5-1 CAPOperationPrepareFunction
  7.5-2 CAPAddPrepareFunction
  7.5-3 ListCAPPrepareFunctions
 7.6 Available Add functions

  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 Managing Derived Methods
 8.1 Info Class

  8.1-1 DerivationInfo
  8.1-2 ActivateDerivationInfo
  8.1-3 DeactivateDerivationInfo
 8.2 Derivation Objects

  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 Derivation Graphs

  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 Managing Derivations in a Category

  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 Min Heaps for Strings

  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 Technical Details
 9.1 The Category Cat

  9.1-1 ObjectCache
  9.1-2 MorphismCache
 9.2 Tools

  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 Limits and Colimits
 10.1 Specification of Limits and Colimits
 10.2 Enhancing Limit Specifications
 10.3 Functions

  10.3-1 CAP_INTERNAL_GENERATE_CONVENIENCE_METHODS_FOR_LIMITS
  10.3-2 CAP_INTERNAL_VALIDATE_LIMITS_IN_NAME_RECORD
11 The Category Constructor
 11.1 Info class

  11.1-1 InfoCategoryConstructor
 11.2 Constructors

  11.2-1 CategoryConstructor
12 Create wrapper hulls of a category
 12.1 GAP categories

  12.1-1 IsWrapperCapCategory
  12.1-2 IsWrapperCapCategoryObject
  12.1-3 IsWrapperCapCategoryMorphism
 12.2 Attributes

  12.2-1 ModelingCategory
  12.2-2 UnderlyingCell
  12.2-3 UnderlyingCell
 12.3 Constructors

  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 Dummy categories
 13.1 GAP categories

  13.1-1 IsDummyCategory
  13.1-2 IsDummyCategoryObject
  13.1-3 IsDummyCategoryMorphism
 13.2 Constructors

  13.2-1 DummyCategory
14 Examples and Tests
 14.1 Dummy category
 14.2 Functors
 14.3 HandlePrecompiledTowers
 14.4 Homomorphism structure
 14.5 Homology object
 14.6 Liftable
 14.7 WrapperCategory
 14.8 Monoidal Categories
 14.9 MorphismFromSourceToPushout and MorphismFromFiberProductToSink
 14.10 Opposite category
 14.11 Terminal category
 14.12 Generalized Morphisms Category
 14.13 IsWellDefined
 14.14 Kernel
 14.15 FiberProduct
15 Terminal category
 15.1 GAP Categories

  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 Constructors

  15.2-1 TerminalCategoryWithSingleObject
  15.2-2 TerminalCategoryWithMultipleObjects
  15.2-3 CAP_INTERNAL_CONSTRUCTOR_FOR_TERMINAL_CATEGORY
 15.3 Attributes

  15.3-1 UniqueObject
  15.3-2 UniqueMorphism
  15.3-3 FunctorFromTerminalCategory
Index

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