Goto Chapter: Top 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Ind
 [Top of Book]  [Contents]   [Next Chapter] 

CAP

Categories, Algorithms, Programming

2023.10-07

20 October 2023

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 Equalities for Objects

  2.2-1 IsEqualForObjects
  2.2-2 IsIsomorphicForObjects
  2.2-3 SomeIsomorphismBetweenObjects
 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
  3.1-4 Target
 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
  3.10-9 LinearCombinationOfMorphisms
 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
  4.1-3 Target
 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 ComponentOfMorphismIntoDirectSum
  6.6-19 ComponentOfMorphismFromDirectSum
  6.6-20 DirectSumFunctorial
  6.6-21 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
  6.7-10 ComponentOfMorphismFromCoproduct
 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
  6.8-9 ComponentOfMorphismIntoDirectProduct
 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
  6.9-11 JointPairwiseDifferencesOfMorphismsIntoDirectProduct
  6.9-12 IsomorphismFromEqualizerToKernelOfJointPairwiseDifferencesOfMorphismsIntoDirectProduct
  6.9-13 IsomorphismFromKernelOfJointPairwiseDifferencesOfMorphismsIntoDirectProductToEqualizer
 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
  6.10-11 JointPairwiseDifferencesOfMorphismsFromCoproduct
  6.10-12 IsomorphismFromCoequalizerToCokernelOfJointPairwiseDifferencesOfMorphismsFromCoproduct
  6.10-13 IsomorphismFromCokernelOfJointPairwiseDifferencesOfMorphismsFromCoproductToCoequalizer
 6.11 Fiber Product

  6.11-1 IsomorphismFromFiberProductToEqualizerOfDirectProductDiagram
  6.11-2 IsomorphismFromEqualizerOfDirectProductDiagramToFiberProduct
  6.11-3 FiberProductEmbeddingInDirectProduct
  6.11-4 FiberProductEmbeddingInDirectSum
  6.11-5 FiberProduct
  6.11-6 FiberProductOp
  6.11-7 ProjectionInFactorOfFiberProduct
  6.11-8 ProjectionInFactorOfFiberProductWithGivenFiberProduct
  6.11-9 MorphismFromFiberProductToSink
  6.11-10 MorphismFromFiberProductToSinkWithGivenFiberProduct
  6.11-11 UniversalMorphismIntoFiberProduct
  6.11-12 UniversalMorphismIntoFiberProductWithGivenFiberProduct
  6.11-13 FiberProductFunctorial
  6.11-14 FiberProductFunctorialWithGivenFiberProducts
 6.12 Pushout

  6.12-1 IsomorphismFromPushoutToCoequalizerOfCoproductDiagram
  6.12-2 IsomorphismFromCoequalizerOfCoproductDiagramToPushout
  6.12-3 PushoutProjectionFromCoproduct
  6.12-4 PushoutProjectionFromDirectSum
  6.12-5 Pushout
  6.12-6 Pushout
  6.12-7 InjectionOfCofactorOfPushout
  6.12-8 InjectionOfCofactorOfPushoutWithGivenPushout
  6.12-9 MorphismFromSourceToPushout
  6.12-10 MorphismFromSourceToPushoutWithGivenPushout
  6.12-11 UniversalMorphismFromPushout
  6.12-12 UniversalMorphismFromPushoutWithGivenPushout
  6.12-13 PushoutFunctorial
  6.12-14 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 InverseOfMorphismFromCoimageToImage
  6.14-4 InverseOfMorphismFromCoimageToImageWithGivenObjects
  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 CoimageObjectFunctorial
  6.14-15 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 AddCoastrictionToImage
  7.6-8 AddCoastrictionToImageWithGivenImageObject
  7.6-9 AddCoefficientsOfMorphism
  7.6-10 AddCoequalizer
  7.6-11 AddCoequalizerFunctorial
  7.6-12 AddCoequalizerFunctorialWithGivenCoequalizers
  7.6-13 AddCoimageObject
  7.6-14 AddCoimageObjectFunctorial
  7.6-15 AddCoimageObjectFunctorialWithGivenCoimageObjects
  7.6-16 AddCoimageProjection
  7.6-17 AddCoimageProjectionWithGivenCoimageObject
  7.6-18 AddCokernelColift
  7.6-19 AddCokernelColiftWithGivenCokernelObject
  7.6-20 AddCokernelObject
  7.6-21 AddCokernelObjectFunctorial
  7.6-22 AddCokernelObjectFunctorialWithGivenCokernelObjects
  7.6-23 AddCokernelProjection
  7.6-24 AddCokernelProjectionWithGivenCokernelObject
  7.6-25 AddColift
  7.6-26 AddColiftAlongEpimorphism
  7.6-27 AddColiftOrFail
  7.6-28 AddComponentOfMorphismFromCoproduct
  7.6-29 AddComponentOfMorphismFromDirectSum
  7.6-30 AddComponentOfMorphismIntoDirectProduct
  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 AddDirectSumFunctorial
  7.6-40 AddDirectSumFunctorialWithGivenDirectSums
  7.6-41 AddDistinguishedObjectOfHomomorphismStructure
  7.6-42 AddEmbeddingOfEqualizer
  7.6-43 AddEmbeddingOfEqualizerWithGivenEqualizer
  7.6-44 AddEpimorphismFromProjectiveCoverObject
  7.6-45 AddEpimorphismFromProjectiveCoverObjectWithGivenProjectiveCoverObject
  7.6-46 AddEpimorphismFromSomeProjectiveObject
  7.6-47 AddEpimorphismFromSomeProjectiveObjectWithGivenSomeProjectiveObject
  7.6-48 AddEqualizer
  7.6-49 AddEqualizerFunctorial
  7.6-50 AddEqualizerFunctorialWithGivenEqualizers
  7.6-51 AddFiberProduct
  7.6-52 AddFiberProductFunctorial
  7.6-53 AddFiberProductFunctorialWithGivenFiberProducts
  7.6-54 AddHomologyObject
  7.6-55 AddHomologyObjectFunctorialWithGivenHomologyObjects
  7.6-56 AddHomomorphismStructureOnMorphisms
  7.6-57 AddHomomorphismStructureOnMorphismsWithGivenObjects
  7.6-58 AddHomomorphismStructureOnObjects
  7.6-59 AddHorizontalPostCompose
  7.6-60 AddHorizontalPreCompose
  7.6-61 AddIdentityMorphism
  7.6-62 AddIdentityTwoCell
  7.6-63 AddImageEmbedding
  7.6-64 AddImageEmbeddingWithGivenImageObject
  7.6-65 AddImageObject
  7.6-66 AddImageObjectFunctorial
  7.6-67 AddImageObjectFunctorialWithGivenImageObjects
  7.6-68 AddIndecomposableInjectiveObjects
  7.6-69 AddIndecomposableProjectiveObjects
  7.6-70 AddInitialObject
  7.6-71 AddInitialObjectFunctorial
  7.6-72 AddInitialObjectFunctorialWithGivenInitialObjects
  7.6-73 AddInjectionOfCofactorOfCoproduct
  7.6-74 AddInjectionOfCofactorOfCoproductWithGivenCoproduct
  7.6-75 AddInjectionOfCofactorOfDirectSum
  7.6-76 AddInjectionOfCofactorOfDirectSumWithGivenDirectSum
  7.6-77 AddInjectionOfCofactorOfPushout
  7.6-78 AddInjectionOfCofactorOfPushoutWithGivenPushout
  7.6-79 AddInjectiveColift
  7.6-80 AddInjectiveDimension
  7.6-81 AddInjectiveEnvelopeObject
  7.6-82 AddInterpretMorphismAsMorphismFromDistinguishedObjectToHomomorphismStructure
  7.6-83 AddInterpretMorphismAsMorphismFromDistinguishedObjectToHomomorphismStructureWithGivenObjects
  7.6-84 AddInterpretMorphismFromDistinguishedObjectToHomomorphismStructureAsMorphism
  7.6-85 AddInverseForMorphisms
  7.6-86 AddInverseOfMorphismFromCoimageToImage
  7.6-87 AddInverseOfMorphismFromCoimageToImageWithGivenObjects
  7.6-88 AddIsAutomorphism
  7.6-89 AddIsBijectiveObject
  7.6-90 AddIsCodominating
  7.6-91 AddIsColiftable
  7.6-92 AddIsColiftableAlongEpimorphism
  7.6-93 AddIsCongruentForMorphisms
  7.6-94 AddIsDominating
  7.6-95 AddIsEndomorphism
  7.6-96 AddIsEpimorphism
  7.6-97 AddIsEqualAsFactorobjects
  7.6-98 AddIsEqualAsSubobjects
  7.6-99 AddIsEqualForCacheForMorphisms
  7.6-100 AddIsEqualForCacheForObjects
  7.6-101 AddIsEqualForMorphisms
  7.6-102 AddIsEqualForMorphismsOnMor
  7.6-103 AddIsEqualForObjects
  7.6-104 AddIsEqualToIdentityMorphism
  7.6-105 AddIsEqualToZeroMorphism
  7.6-106 AddIsHomSetInhabited
  7.6-107 AddIsIdempotent
  7.6-108 AddIsInitial
  7.6-109 AddIsInjective
  7.6-110 AddIsIsomorphicForObjects
  7.6-111 AddIsIsomorphism
  7.6-112 AddIsLiftable
  7.6-113 AddIsLiftableAlongMonomorphism
  7.6-114 AddIsMonomorphism
  7.6-115 AddIsOne
  7.6-116 AddIsProjective
  7.6-117 AddIsSplitEpimorphism
  7.6-118 AddIsSplitMonomorphism
  7.6-119 AddIsTerminal
  7.6-120 AddIsWellDefinedForMorphisms
  7.6-121 AddIsWellDefinedForObjects
  7.6-122 AddIsWellDefinedForTwoCells
  7.6-123 AddIsZeroForMorphisms
  7.6-124 AddIsZeroForObjects
  7.6-125 AddIsomorphismFromCoequalizerOfCoproductDiagramToPushout
  7.6-126 AddIsomorphismFromCoequalizerToCokernelOfJointPairwiseDifferencesOfMorphismsFromCoproduct
  7.6-127 AddIsomorphismFromCoimageToCokernelOfKernel
  7.6-128 AddIsomorphismFromCokernelOfJointPairwiseDifferencesOfMorphismsFromCoproductToCoequalizer
  7.6-129 AddIsomorphismFromCokernelOfKernelToCoimage
  7.6-130 AddIsomorphismFromCoproductToDirectSum
  7.6-131 AddIsomorphismFromDirectProductToDirectSum
  7.6-132 AddIsomorphismFromDirectSumToCoproduct
  7.6-133 AddIsomorphismFromDirectSumToDirectProduct
  7.6-134 AddIsomorphismFromEqualizerOfDirectProductDiagramToFiberProduct
  7.6-135 AddIsomorphismFromEqualizerToKernelOfJointPairwiseDifferencesOfMorphismsIntoDirectProduct
  7.6-136 AddIsomorphismFromFiberProductToEqualizerOfDirectProductDiagram
  7.6-137 AddIsomorphismFromHomologyObjectToItsConstructionAsAnImageObject
  7.6-138 AddIsomorphismFromImageObjectToKernelOfCokernel
  7.6-139 AddIsomorphismFromInitialObjectToZeroObject
  7.6-140 AddIsomorphismFromItsConstructionAsAnImageObjectToHomologyObject
  7.6-141 AddIsomorphismFromKernelOfCokernelToImageObject
  7.6-142 AddIsomorphismFromKernelOfJointPairwiseDifferencesOfMorphismsIntoDirectProductToEqualizer
  7.6-143 AddIsomorphismFromPushoutToCoequalizerOfCoproductDiagram
  7.6-144 AddIsomorphismFromTerminalObjectToZeroObject
  7.6-145 AddIsomorphismFromZeroObjectToInitialObject
  7.6-146 AddIsomorphismFromZeroObjectToTerminalObject
  7.6-147 AddJointPairwiseDifferencesOfMorphismsFromCoproduct
  7.6-148 AddJointPairwiseDifferencesOfMorphismsIntoDirectProduct
  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 AddLinearCombinationOfMorphisms
  7.6-160 AddMereExistenceOfSolutionOfLinearSystemInAbCategory
  7.6-161 AddMonomorphismIntoInjectiveEnvelopeObject
  7.6-162 AddMonomorphismIntoInjectiveEnvelopeObjectWithGivenInjectiveEnvelopeObject
  7.6-163 AddMonomorphismIntoSomeInjectiveObject
  7.6-164 AddMonomorphismIntoSomeInjectiveObjectWithGivenSomeInjectiveObject
  7.6-165 AddMorphismBetweenDirectSums
  7.6-166 AddMorphismBetweenDirectSumsWithGivenDirectSums
  7.6-167 AddMorphismConstructor
  7.6-168 AddMorphismDatum
  7.6-169 AddMorphismFromCoimageToImage
  7.6-170 AddMorphismFromCoimageToImageWithGivenObjects
  7.6-171 AddMorphismFromEqualizerToSink
  7.6-172 AddMorphismFromEqualizerToSinkWithGivenEqualizer
  7.6-173 AddMorphismFromFiberProductToSink
  7.6-174 AddMorphismFromFiberProductToSinkWithGivenFiberProduct
  7.6-175 AddMorphismFromKernelObjectToSink
  7.6-176 AddMorphismFromKernelObjectToSinkWithGivenKernelObject
  7.6-177 AddMorphismFromSourceToCoequalizer
  7.6-178 AddMorphismFromSourceToCoequalizerWithGivenCoequalizer
  7.6-179 AddMorphismFromSourceToCokernelObject
  7.6-180 AddMorphismFromSourceToCokernelObjectWithGivenCokernelObject
  7.6-181 AddMorphismFromSourceToPushout
  7.6-182 AddMorphismFromSourceToPushoutWithGivenPushout
  7.6-183 AddMultiplyWithElementOfCommutativeRingForMorphisms
  7.6-184 AddObjectConstructor
  7.6-185 AddObjectDatum
  7.6-186 AddPostCompose
  7.6-187 AddPostComposeList
  7.6-188 AddPostInverseForMorphisms
  7.6-189 AddPreCompose
  7.6-190 AddPreComposeList
  7.6-191 AddPreInverseForMorphisms
  7.6-192 AddProjectionInFactorOfDirectProduct
  7.6-193 AddProjectionInFactorOfDirectProductWithGivenDirectProduct
  7.6-194 AddProjectionInFactorOfDirectSum
  7.6-195 AddProjectionInFactorOfDirectSumWithGivenDirectSum
  7.6-196 AddProjectionInFactorOfFiberProduct
  7.6-197 AddProjectionInFactorOfFiberProductWithGivenFiberProduct
  7.6-198 AddProjectionOntoCoequalizer
  7.6-199 AddProjectionOntoCoequalizerWithGivenCoequalizer
  7.6-200 AddProjectiveCoverObject
  7.6-201 AddProjectiveDimension
  7.6-202 AddProjectiveLift
  7.6-203 AddPushout
  7.6-204 AddPushoutFunctorial
  7.6-205 AddPushoutFunctorialWithGivenPushouts
  7.6-206 AddRandomMorphismByInteger
  7.6-207 AddRandomMorphismByList
  7.6-208 AddRandomMorphismWithFixedRangeByInteger
  7.6-209 AddRandomMorphismWithFixedRangeByList
  7.6-210 AddRandomMorphismWithFixedSourceAndRangeByInteger
  7.6-211 AddRandomMorphismWithFixedSourceAndRangeByList
  7.6-212 AddRandomMorphismWithFixedSourceByInteger
  7.6-213 AddRandomMorphismWithFixedSourceByList
  7.6-214 AddRandomObjectByInteger
  7.6-215 AddRandomObjectByList
  7.6-216 AddSimplifyEndo
  7.6-217 AddSimplifyEndo_IsoFromInputObject
  7.6-218 AddSimplifyEndo_IsoToInputObject
  7.6-219 AddSimplifyMorphism
  7.6-220 AddSimplifyObject
  7.6-221 AddSimplifyObject_IsoFromInputObject
  7.6-222 AddSimplifyObject_IsoToInputObject
  7.6-223 AddSimplifyRange
  7.6-224 AddSimplifyRange_IsoFromInputObject
  7.6-225 AddSimplifyRange_IsoToInputObject
  7.6-226 AddSimplifySource
  7.6-227 AddSimplifySourceAndRange
  7.6-228 AddSimplifySourceAndRange_IsoFromInputRange
  7.6-229 AddSimplifySourceAndRange_IsoFromInputSource
  7.6-230 AddSimplifySourceAndRange_IsoToInputRange
  7.6-231 AddSimplifySourceAndRange_IsoToInputSource
  7.6-232 AddSimplifySource_IsoFromInputObject
  7.6-233 AddSimplifySource_IsoToInputObject
  7.6-234 AddSolveLinearSystemInAbCategory
  7.6-235 AddSolveLinearSystemInAbCategoryOrFail
  7.6-236 AddSomeInjectiveObject
  7.6-237 AddSomeIsomorphismBetweenObjects
  7.6-238 AddSomeProjectiveObject
  7.6-239 AddSomeReductionBySplitEpiSummand
  7.6-240 AddSomeReductionBySplitEpiSummand_MorphismFromInputRange
  7.6-241 AddSomeReductionBySplitEpiSummand_MorphismToInputRange
  7.6-242 AddSubtractionForMorphisms
  7.6-243 AddSumOfMorphisms
  7.6-244 AddTerminalObject
  7.6-245 AddTerminalObjectFunctorial
  7.6-246 AddTerminalObjectFunctorialWithGivenTerminalObjects
  7.6-247 AddUniversalMorphismFromCoequalizer
  7.6-248 AddUniversalMorphismFromCoequalizerWithGivenCoequalizer
  7.6-249 AddUniversalMorphismFromCoproduct
  7.6-250 AddUniversalMorphismFromCoproductWithGivenCoproduct
  7.6-251 AddUniversalMorphismFromDirectSum
  7.6-252 AddUniversalMorphismFromDirectSumWithGivenDirectSum
  7.6-253 AddUniversalMorphismFromImage
  7.6-254 AddUniversalMorphismFromImageWithGivenImageObject
  7.6-255 AddUniversalMorphismFromInitialObject
  7.6-256 AddUniversalMorphismFromInitialObjectWithGivenInitialObject
  7.6-257 AddUniversalMorphismFromPushout
  7.6-258 AddUniversalMorphismFromPushoutWithGivenPushout
  7.6-259 AddUniversalMorphismFromZeroObject
  7.6-260 AddUniversalMorphismFromZeroObjectWithGivenZeroObject
  7.6-261 AddUniversalMorphismIntoCoimage
  7.6-262 AddUniversalMorphismIntoCoimageWithGivenCoimageObject
  7.6-263 AddUniversalMorphismIntoDirectProduct
  7.6-264 AddUniversalMorphismIntoDirectProductWithGivenDirectProduct
  7.6-265 AddUniversalMorphismIntoDirectSum
  7.6-266 AddUniversalMorphismIntoDirectSumWithGivenDirectSum
  7.6-267 AddUniversalMorphismIntoEqualizer
  7.6-268 AddUniversalMorphismIntoEqualizerWithGivenEqualizer
  7.6-269 AddUniversalMorphismIntoFiberProduct
  7.6-270 AddUniversalMorphismIntoFiberProductWithGivenFiberProduct
  7.6-271 AddUniversalMorphismIntoTerminalObject
  7.6-272 AddUniversalMorphismIntoTerminalObjectWithGivenTerminalObject
  7.6-273 AddUniversalMorphismIntoZeroObject
  7.6-274 AddUniversalMorphismIntoZeroObjectWithGivenZeroObject
  7.6-275 AddVerticalPostCompose
  7.6-276 AddVerticalPreCompose
  7.6-277 AddZeroMorphism
  7.6-278 AddZeroObject
  7.6-279 AddZeroObjectFunctorial
  7.6-280 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 AddDerivationToCAP
  8.3-7 AddWithGivenDerivationPairToCAP
  8.3-8 Operations
  8.3-9 DerivationsUsingOperation
  8.3-10 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 CAP_INTERNAL_GET_DATA_TYPE_FROM_STRING
  9.2-2 CAP_INTERNAL_GET_DATA_TYPES_FROM_STRINGS
  9.2-3 CAP_INTERNAL_REPLACED_STRING_WITH_FILTER
  9.2-4 CAP_INTERNAL_REPLACED_STRINGS_WITH_FILTERS
  9.2-5 CAP_INTERNAL_MERGE_FILTER_LISTS
  9.2-6 CAP_INTERNAL_RETURN_OPTION_OR_DEFAULT
  9.2-7 CAP_INTERNAL_FIND_APPEARANCE_OF_SYMBOL_IN_FUNCTION
  9.2-8 CAP_INTERNAL_MERGE_PRECONDITIONS_LIST
  9.2-9 CAP_INTERNAL_ASSERT_VALUE_IS_OF_TYPE_GETTER
  9.2-10 CAP_INTERNAL_ASSERT_IS_CELL_OF_CATEGORY
  9.2-11 CAP_INTERNAL_ASSERT_IS_OBJECT_OF_CATEGORY
  9.2-12 CAP_INTERNAL_ASSERT_IS_MORPHISM_OF_CATEGORY
  9.2-13 CAP_INTERNAL_ASSERT_IS_TWO_CELL_OF_CATEGORY
  9.2-14 CachingStatistic
  9.2-15 BrowseCachingStatistic
  9.2-16 InstallDeprecatedAlias
  9.2-17 IsSpecializationOfFilter
  9.2-18 IsSpecializationOfFilterList
  9.2-19 InstallMethodForCompilerForCAP
  9.2-20 InstallOtherMethodForCompilerForCAP
  9.2-21 CapJitAddKnownMethod
  9.2-22 CapJitAddTypeSignature
  9.2-23 CapJitAddTypeSignatureDeferred
  9.2-24 CapJitDataTypeOfListOf
  9.2-25 CapJitDataTypeOfNTupleOf
  9.2-26 CapJitDataTypeOfCategory
  9.2-27 CapFixpoint
  9.2-28 Iterated
  9.2-29 Iterated
  9.2-30 TransitivelyNeededOtherPackages
  9.2-31 PackageOfCAPOperation
  9.2-32 SafePosition
  9.2-33 SafeUniquePosition
  9.2-34 SafePositionProperty
  9.2-35 SafeUniquePositionProperty
  9.2-36 SafeFirst
  9.2-37 SafeUniqueEntry
  9.2-38 NTuple
  9.2-39 Pair
  9.2-40 Triple
  9.2-41 TransposedMatWithGivenDimensions
  9.2-42 HandlePrecompiledTowers
  9.2-43 CAP_JIT_INCOMPLETE_LOGIC
  9.2-44 ListWithKeys
  9.2-45 SumWithKeys
  9.2-46 ProductWithKeys
  9.2-47 ForAllWithKeys
  9.2-48 ForAnyWithKeys
  9.2-49 NumberWithKeys
  9.2-50 FilteredWithKeys
  9.2-51 FirstWithKeys
  9.2-52 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 Reinterpretations of categories
 12.1 Introduction
 12.2 Tutorial
 12.3 Implementation details
 12.4 Relation to CompilerForCAP
 12.5 Attributes

  12.5-1 ModelingCategory
 12.6 Constructors

  12.6-1 ReinterpretationOfCategory
  12.6-2 ReinterpretationFunctor
  12.6-3 ModelingObject
  12.6-4 ReinterpretationOfObject
  12.6-5 ModelingMorphism
  12.6-6 ReinterpretationOfMorphism
13 Create wrapper hulls of a category
 13.1 GAP categories

  13.1-1 IsWrapperCapCategory
  13.1-2 IsWrapperCapCategoryObject
  13.1-3 IsWrapperCapCategoryMorphism
 13.2 Attributes

  13.2-1 UnderlyingCell
  13.2-2 UnderlyingCell
 13.3 Constructors

  13.3-1 AsObjectInWrapperCategory
  13.3-2 AsMorphismInWrapperCategory
  13.3-3 AsMorphismInWrapperCategory
  13.3-4 /
  13.3-5 WrapperCategory
  13.3-6 WrappingFunctor
14 Dummy categories
 14.1 GAP categories

  14.1-1 IsDummyCategory
  14.1-2 IsDummyCategoryObject
  14.1-3 IsDummyCategoryMorphism
 14.2 Constructors

  14.2-1 DummyCategory
15 Examples and Tests
 15.1 Dummy category
 15.2 Functors
 15.3 HandlePrecompiledTowers
 15.4 Homomorphism structure
 15.5 Homology object
 15.6 Liftable
 15.7 Monoidal Categories
 15.8 MorphismFromSourceToPushout and MorphismFromFiberProductToSink
 15.9 Opposite category
 15.10 PreComposeList and PostComposeList
 15.11 Terminal category
 15.12 WrapperCategory
16 Terminal category
 16.1 GAP Categories

  16.1-1 IsCapTerminalCategoryWithSingleObject
  16.1-2 IsObjectInCapTerminalCategoryWithSingleObject
  16.1-3 IsMorphismInCapTerminalCategoryWithSingleObject
  16.1-4 IsCapTerminalCategoryWithMultipleObjects
  16.1-5 IsObjectInCapTerminalCategoryWithMultipleObjects
  16.1-6 IsMorphismInCapTerminalCategoryWithMultipleObjects
  16.1-7 IsTerminalCategory
 16.2 Constructors

  16.2-1 TerminalCategoryWithSingleObject
  16.2-2 TerminalCategoryWithMultipleObjects
  16.2-3 CAP_INTERNAL_CONSTRUCTOR_FOR_TERMINAL_CATEGORY
 16.3 Attributes

  16.3-1 UniqueObject
  16.3-2 UniqueMorphism
  16.3-3 FunctorFromTerminalCategory
Index

 [Top of Book]  [Contents]   [Next Chapter] 
Goto Chapter: Top 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Ind

generated by GAPDoc2HTML