  
  
                                     [1X CAP [101X
  
  
                     [1X Categories, Algorithms, Programming [101X
  
  
                                   2016.02.19
  
  
                                   19/02/2016
  
  
                               Sebastian Gutsche
  
                                Sebastian Posur
  
                            Øystein Skartsæterhagen
  
  
  
  Sebastian Gutsche
      Email:    [7Xmailto:gutsche@mathematik.uni-kl.de[107X
      Homepage: [7Xhttp://wwwb.math.rwth-aachen.de/~gutsche[107X
      Address:  [33X[0;14YTODO[133X
  
  
  Sebastian Posur
      Email:    [7Xmailto:sposur@momo.math.rwth-aachen.de[107X
      Homepage: [7Xhttp://wwwb.math.rwth-aachen.de/Mitarbeiter/posur.php[107X
      Address:  [33X[0;14YLehrstuhl B für Mathematik RWTH - Aachen[133X
                [33X[0;14YTemplergraben 64[133X
                [33X[0;14Y52062 Aachen[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;0YConstructor[133X
      1.2-1 CreateCapCategory
      1.2-2 CreateCapCategory
    1.3 [33X[0;0YInternal Attributes[133X
      1.3-1 CategoryFilter
      1.3-2 CellFilter
      1.3-3 ObjectFilter
      1.3-4 MorphismFilter
      1.3-5 TwoCellFilter
    1.4 [33X[0;0YLogic switcher[133X
      1.4-1 CapCategorySwitchLogicOn
      1.4-2 CapCategorySwitchLogicOff
    1.5 [33X[0;0YTool functions[133X
      1.5-1 CanCompute
      1.5-2 CheckConstructivenessOfCategory
    1.6 [33X[0;0YWell-Definedness of Cells[133X
      1.6-1 IsWellDefined
    1.7 [33X[0;0YType check[133X
      1.7-1 DisableBasicOperationTypeCheck
  2 [33X[0;0YCategory of Categories[133X
    2.1 [33X[0;0YThe Category Cat[133X
      2.1-1 CapCat
    2.2 [33X[0;0YCategories[133X
      2.2-1 IsCapCategoryAsCatObject
      2.2-2 IsCapFunctor
      2.2-3 IsCapNaturalTransformation
    2.3 [33X[0;0YConstructors[133X
      2.3-1 AsCatObject
      2.3-2 AsCapCategory
    2.4 [33X[0;0YFunctors[133X
      2.4-1 CapFunctor
      2.4-2 AddObjectFunction
      2.4-3 FunctorObjectOperation
      2.4-4 AddMorphismFunction
      2.4-5 FunctorMorphismOperation
      2.4-6 ApplyFunctor
      2.4-7 InstallFunctor
    2.5 [33X[0;0YNatural transformations[133X
      2.5-1 Name
      2.5-2 NaturalTransformation
      2.5-3 AddNaturalTransformationFunction
      2.5-4 ApplyNaturalTransformation
      2.5-5 InstallNaturalTransformation
      2.5-6 HorizontalPreComposeNaturalTransformationWithFunctor
      2.5-7 HorizontalPreComposeFunctorWithNaturalTransformation
  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;0YCategorical Properties of Morphisms[133X
      3.2-1 AddIsMonomorphism
      3.2-2 AddIsEpimorphism
      3.2-3 AddIsIsomorphism
      3.2-4 AddIsSplitMonomorphism
      3.2-5 AddIsSplitEpimorphism
      3.2-6 AddIsOne
      3.2-7 AddIsIdempotent
    3.3 [33X[0;0YNon-Categorical Properties of Morphisms[133X
      3.3-1 IsIdenticalToIdentityMorphism
      3.3-2 AddIsIdenticalToIdentityMorphism
      3.3-3 IsIdenticalToZeroMorphism
      3.3-4 AddIsIdenticalToZeroMorphism
      3.3-5 AddIsEndomorphism
      3.3-6 AddIsAutomorphism
    3.4 [33X[0;0YEquality and Congruence for Morphisms[133X
      3.4-1 IsCongruentForMorphisms
      3.4-2 AddIsCongruentForMorphisms
      3.4-3 IsEqualForMorphisms
      3.4-4 AddIsEqualForMorphisms
      3.4-5 IsEqualForMorphismsOnMor
      3.4-6 AddIsEqualForMorphismsOnMor
    3.5 [33X[0;0YBasic Operations for Morphisms in Ab-Categories[133X
      3.5-1 IsZeroForMorphisms
      3.5-2 AddIsZeroForMorphisms
      3.5-3 AdditionForMorphisms
      3.5-4 AddAdditionForMorphisms
      3.5-5 AdditiveInverseForMorphisms
      3.5-6 AddAdditiveInverseForMorphisms
      3.5-7 ZeroMorphism
      3.5-8 AddZeroMorphism
    3.6 [33X[0;0YSubobject and Factorobject Operations[133X
      3.6-1 IsEqualAsSubobjects
      3.6-2 AddIsEqualAsSubobjects
      3.6-3 IsEqualAsFactorobjects
      3.6-4 AddIsEqualAsFactorobjects
      3.6-5 IsDominating
      3.6-6 AddIsDominating
      3.6-7 IsCodominating
      3.6-8 AddIsCodominating
    3.7 [33X[0;0YIdentity Morphism and Composition of Morphisms[133X
      3.7-1 IdentityMorphism
      3.7-2 AddIdentityMorphism
      3.7-3 PreCompose
      3.7-4 PreCompose
      3.7-5 AddPreCompose
      3.7-6 PostCompose
      3.7-7 PostCompose
      3.7-8 AddPostCompose
    3.8 [33X[0;0YWell-Definedness of Morphisms[133X
      3.8-1 IsWellDefinedForMorphisms
      3.8-2 AddIsWellDefinedForMorphisms
    3.9 [33X[0;0YBasic Operations for Morphisms in Abelian Categories[133X
      3.9-1 LiftAlongMonomorphism
      3.9-2 AddLiftAlongMonomorphism
      3.9-3 ColiftAlongEpimorphism
      3.9-4 AddColiftAlongEpimorphism
    3.10 [33X[0;0YLift/ Colift[133X
      3.10-1 Lift
      3.10-2 AddLift
      3.10-3 Colift
      3.10-4 AddColift
    3.11 [33X[0;0YInverses[133X
      3.11-1 AddInverse
    3.12 [33X[0;0YTool functions for caches[133X
      3.12-1 IsEqualForCacheForMorphisms
      3.12-2 AddIsEqualForCacheForMorphisms
  4 [33X[0;0YObjects[133X
    4.1 [33X[0;0YAttributes for the Type of Objects[133X
      4.1-1 CapCategory
    4.2 [33X[0;0YEquality for Objects[133X
      4.2-1 IsEqualForObjects
      4.2-2 AddIsEqualForObjects
    4.3 [33X[0;0YCategorical Properties of Objects[133X
      4.3-1 AddIsProjective
      4.3-2 AddIsInjective
      4.3-3 AddIsTerminal
      4.3-4 AddIsInitial
      4.3-5 IsZeroForObjects
      4.3-6 AddIsZeroForObjects
    4.4 [33X[0;0YTool functions for caches[133X
      4.4-1 IsEqualForCacheForObjects
      4.4-2 AddIsEqualForCacheForObjects
    4.5 [33X[0;0YWell-Definedness of Objects[133X
      4.5-1 IsWellDefinedForObjects
      4.5-2 AddIsWellDefinedForObjects
  5 [33X[0;0YCategory 2-Cells[133X
    5.1 [33X[0;0YAttributes for the Type of 2-Cells[133X
      5.1-1 Source
      5.1-2 Range
    5.2 [33X[0;0YIdentity 2-Cell and Composition of 2-Cells[133X
      5.2-1 IdentityTwoCell
      5.2-2 AddIdentityTwoCell
      5.2-3 HorizontalPreCompose
      5.2-4 AddHorizontalPreCompose
      5.2-5 HorizontalPostCompose
      5.2-6 AddHorizontalPostCompose
      5.2-7 VerticalPreCompose
      5.2-8 AddVerticalPreCompose
      5.2-9 VerticalPostCompose
      5.2-10 AddVerticalPostCompose
    5.3 [33X[0;0YWell-Definedness for 2-Cells[133X
      5.3-1 IsWellDefinedForTwoCells
      5.3-2 AddIsWellDefinedForTwoCells
  6 [33X[0;0YUniversal Objects[133X
    6.1 [33X[0;0YKernel[133X
      6.1-1 KernelObject
      6.1-2 KernelEmbedding
      6.1-3 KernelEmbedding
      6.1-4 KernelEmbeddingWithGivenKernelObject
      6.1-5 KernelLift
      6.1-6 KernelLift
      6.1-7 KernelLiftWithGivenKernelObject
      6.1-8 AddKernelObject
      6.1-9 AddKernelEmbedding
      6.1-10 AddKernelEmbeddingWithGivenKernelObject
      6.1-11 AddKernelLift
      6.1-12 AddKernelLiftWithGivenKernelObject
      6.1-13 KernelObjectFunctorial
      6.1-14 KernelObjectFunctorial
      6.1-15 AddKernelObjectFunctorial
    6.2 [33X[0;0YCokernel[133X
      6.2-1 CokernelObject
      6.2-2 CokernelProjection
      6.2-3 CokernelProjection
      6.2-4 CokernelProjectionWithGivenCokernelObject
      6.2-5 CokernelColift
      6.2-6 CokernelColift
      6.2-7 CokernelColiftWithGivenCokernelObject
      6.2-8 AddCokernelObject
      6.2-9 AddCokernelProjection
      6.2-10 AddCokernelProjectionWithGivenCokernelObject
      6.2-11 AddCokernelColift
      6.2-12 AddCokernelColiftWithGivenCokernelObject
      6.2-13 CokernelFunctorial
      6.2-14 CokernelFunctorial
      6.2-15 AddCokernelFunctorial
    6.3 [33X[0;0YZero Object[133X
      6.3-1 ZeroObject
      6.3-2 ZeroObject
      6.3-3 MorphismFromZeroObject
      6.3-4 MorphismIntoZeroObject
      6.3-5 UniversalMorphismFromZeroObject
      6.3-6 UniversalMorphismFromZeroObjectWithGivenZeroObject
      6.3-7 UniversalMorphismIntoZeroObject
      6.3-8 UniversalMorphismIntoZeroObjectWithGivenZeroObject
      6.3-9 IsomorphismFromZeroObjectToInitialObject
      6.3-10 IsomorphismFromInitialObjectToZeroObject
      6.3-11 IsomorphismFromZeroObjectToTerminalObject
      6.3-12 IsomorphismFromTerminalObjectToZeroObject
      6.3-13 AddZeroObject
      6.3-14 AddUniversalMorphismIntoZeroObject
      6.3-15 AddUniversalMorphismIntoZeroObjectWithGivenZeroObject
      6.3-16 AddUniversalMorphismFromZeroObject
      6.3-17 AddUniversalMorphismFromZeroObjectWithGivenZeroObject
      6.3-18 AddIsomorphismFromZeroObjectToInitialObject
      6.3-19 AddIsomorphismFromInitialObjectToZeroObject
      6.3-20 AddIsomorphismFromZeroObjectToTerminalObject
      6.3-21 AddIsomorphismFromTerminalObjectToZeroObject
    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 AddTerminalObject
      6.4-6 AddUniversalMorphismIntoTerminalObject
      6.4-7 AddUniversalMorphismIntoTerminalObjectWithGivenTerminalObject
      6.4-8 TerminalObjectFunctorial
      6.4-9 AddTerminalObjectFunctorial
    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 AddInitialObject
      6.5-6 AddUniversalMorphismFromInitialObject
      6.5-7 AddUniversalMorphismFromInitialObjectWithGivenInitialObject
      6.5-8 InitialObjectFunctorial
      6.5-9 AddInitialObjectFunctorial
    6.6 [33X[0;0YDirect Sum[133X
      6.6-1 DirectSumOp
      6.6-2 ProjectionInFactorOfDirectSum
      6.6-3 ProjectionInFactorOfDirectSumOp
      6.6-4 ProjectionInFactorOfDirectSumWithGivenDirectSum
      6.6-5 InjectionOfCofactorOfDirectSum
      6.6-6 InjectionOfCofactorOfDirectSumOp
      6.6-7 InjectionOfCofactorOfDirectSumWithGivenDirectSum
      6.6-8 UniversalMorphismIntoDirectSum
      6.6-9 UniversalMorphismIntoDirectSumOp
      6.6-10 UniversalMorphismIntoDirectSumWithGivenDirectSum
      6.6-11 UniversalMorphismFromDirectSum
      6.6-12 UniversalMorphismFromDirectSumOp
      6.6-13 UniversalMorphismFromDirectSumWithGivenDirectSum
      6.6-14 IsomorphismFromDirectSumToDirectProduct
      6.6-15 IsomorphismFromDirectSumToDirectProductOp
      6.6-16 IsomorphismFromDirectProductToDirectSum
      6.6-17 IsomorphismFromDirectProductToDirectSumOp
      6.6-18 IsomorphismFromDirectSumToCoproduct
      6.6-19 IsomorphismFromDirectSumToCoproductOp
      6.6-20 IsomorphismFromCoproductToDirectSum
      6.6-21 IsomorphismFromCoproductToDirectSumOp
      6.6-22 MorphismBetweenDirectSums
      6.6-23 MorphismBetweenDirectSumsOp
      6.6-24 AddProjectionInFactorOfDirectSum
      6.6-25 AddProjectionInFactorOfDirectSumWithGivenDirectSum
      6.6-26 AddInjectionOfCofactorOfDirectSum
      6.6-27 AddInjectionOfCofactorOfDirectSumWithGivenDirectSum
      6.6-28 AddUniversalMorphismIntoDirectSum
      6.6-29 AddUniversalMorphismIntoDirectSumWithGivenDirectSum
      6.6-30 AddUniversalMorphismFromDirectSum
      6.6-31 AddUniversalMorphismFromDirectSumWithGivenDirectSum
      6.6-32 AddIsomorphismFromDirectSumToDirectProduct
      6.6-33 AddIsomorphismFromDirectProductToDirectSum
      6.6-34 AddIsomorphismFromDirectSumToCoproduct
      6.6-35 AddIsomorphismFromCoproductToDirectSum
      6.6-36 AddDirectSum
      6.6-37 DirectSumFunctorial
      6.6-38 AddDirectSumFunctorial
      6.6-39 DirectSumFunctorialOp
    6.7 [33X[0;0YCoproduct[133X
      6.7-1 Coproduct
      6.7-2 Coproduct
      6.7-3 Coproduct
      6.7-4 CoproductOp
      6.7-5 InjectionOfCofactorOfCoproduct
      6.7-6 InjectionOfCofactorOfCoproductOp
      6.7-7 InjectionOfCofactorOfCoproductWithGivenCoproduct
      6.7-8 UniversalMorphismFromCoproduct
      6.7-9 UniversalMorphismFromCoproductOp
      6.7-10 UniversalMorphismFromCoproductWithGivenCoproduct
      6.7-11 AddCoproduct
      6.7-12 AddInjectionOfCofactorOfCoproduct
      6.7-13 AddInjectionOfCofactorOfCoproductWithGivenCoproduct
      6.7-14 AddUniversalMorphismFromCoproduct
      6.7-15 AddUniversalMorphismFromCoproductWithGivenCoproduct
      6.7-16 CoproductFunctorial
      6.7-17 AddCoproductFunctorial
      6.7-18 CoproductFunctorialOp
    6.8 [33X[0;0YDirect Product[133X
      6.8-1 DirectProductOp
      6.8-2 ProjectionInFactorOfDirectProduct
      6.8-3 ProjectionInFactorOfDirectProductOp
      6.8-4 ProjectionInFactorOfDirectProductWithGivenDirectProduct
      6.8-5 UniversalMorphismIntoDirectProduct
      6.8-6 UniversalMorphismIntoDirectProductOp
      6.8-7 UniversalMorphismIntoDirectProductWithGivenDirectProduct
      6.8-8 AddDirectProduct
      6.8-9 AddProjectionInFactorOfDirectProduct
      6.8-10 AddProjectionInFactorOfDirectProductWithGivenDirectProduct
      6.8-11 AddUniversalMorphismIntoDirectProduct
      6.8-12 AddUniversalMorphismIntoDirectProductWithGivenDirectProduct
      6.8-13 DirectProductFunctorial
      6.8-14 AddDirectProductFunctorial
      6.8-15 DirectProductFunctorialOp
    6.9 [33X[0;0YFiber Product[133X
      6.9-1 IsomorphismFromFiberProductToKernelOfDiagonalDifference
      6.9-2 IsomorphismFromFiberProductToKernelOfDiagonalDifferenceOp
      6.9-3 AddIsomorphismFromFiberProductToKernelOfDiagonalDifference
      6.9-4 IsomorphismFromKernelOfDiagonalDifferenceToFiberProduct
      6.9-5 IsomorphismFromKernelOfDiagonalDifferenceToFiberProductOp
      6.9-6 AddIsomorphismFromKernelOfDiagonalDifferenceToFiberProduct
      6.9-7 DirectSumDiagonalDifference
      6.9-8 DirectSumDiagonalDifferenceOp
      6.9-9 AddDirectSumDiagonalDifference
      6.9-10 FiberProductEmbeddingInDirectSum
      6.9-11 FiberProductEmbeddingInDirectSumOp
      6.9-12 AddFiberProductEmbeddingInDirectSum
      6.9-13 FiberProduct
      6.9-14 FiberProductOp
      6.9-15 ProjectionInFactorOfFiberProduct
      6.9-16 ProjectionInFactorOfFiberProductOp
      6.9-17 ProjectionInFactorOfFiberProductWithGivenFiberProduct
      6.9-18 UniversalMorphismIntoFiberProduct
      6.9-19 UniversalMorphismIntoFiberProductOp
      6.9-20 UniversalMorphismIntoFiberProductWithGivenFiberProduct
      6.9-21 AddFiberProduct
      6.9-22 AddProjectionInFactorOfFiberProduct
      6.9-23 AddProjectionInFactorOfFiberProductWithGivenFiberProduct
      6.9-24 AddUniversalMorphismIntoFiberProduct
      6.9-25 AddUniversalMorphismIntoFiberProductWithGivenFiberProduct
      6.9-26 FiberProductFunctorial
      6.9-27 AddFiberProductFunctorial
      6.9-28 FiberProductFunctorialOp
    6.10 [33X[0;0YPushout[133X
      6.10-1 IsomorphismFromPushoutToCokernelOfDiagonalDifference
      6.10-2 IsomorphismFromPushoutToCokernelOfDiagonalDifferenceOp
      6.10-3 AddIsomorphismFromPushoutToCokernelOfDiagonalDifference
      6.10-4 IsomorphismFromCokernelOfDiagonalDifferenceToPushout
      6.10-5 IsomorphismFromCokernelOfDiagonalDifferenceToPushoutOp
      6.10-6 AddIsomorphismFromCokernelOfDiagonalDifferenceToPushout
      6.10-7 DirectSumCodiagonalDifference
      6.10-8 DirectSumCodiagonalDifferenceOp
      6.10-9 AddDirectSumCodiagonalDifference
      6.10-10 DirectSumProjectionInPushout
      6.10-11 DirectSumProjectionInPushoutOp
      6.10-12 AddDirectSumProjectionInPushout
      6.10-13 Pushout
      6.10-14 Pushout
      6.10-15 PushoutOp
      6.10-16 InjectionOfCofactorOfPushout
      6.10-17 InjectionOfCofactorOfPushoutOp
      6.10-18 InjectionOfCofactorOfPushoutWithGivenPushout
      6.10-19 UniversalMorphismFromPushout
      6.10-20 UniversalMorphismFromPushoutOp
      6.10-21 UniversalMorphismFromPushoutWithGivenPushout
      6.10-22 AddPushout
      6.10-23 AddInjectionOfCofactorOfPushout
      6.10-24 AddInjectionOfCofactorOfPushoutWithGivenPushout
      6.10-25 AddUniversalMorphismFromPushout
      6.10-26 AddUniversalMorphismFromPushoutWithGivenPushout
      6.10-27 PushoutFunctorial
      6.10-28 AddPushoutFunctorial
      6.10-29 PushoutFunctorialOp
    6.11 [33X[0;0YImage[133X
      6.11-1 IsomorphismFromImageObjectToKernelOfCokernel
      6.11-2 AddIsomorphismFromImageObjectToKernelOfCokernel
      6.11-3 IsomorphismFromKernelOfCokernelToImageObject
      6.11-4 AddIsomorphismFromKernelOfCokernelToImageObject
      6.11-5 ImageObject
      6.11-6 ImageEmbedding
      6.11-7 ImageEmbedding
      6.11-8 ImageEmbeddingWithGivenImageObject
      6.11-9 CoastrictionToImage
      6.11-10 CoastrictionToImage
      6.11-11 CoastrictionToImageWithGivenImageObject
      6.11-12 UniversalMorphismFromImage
      6.11-13 UniversalMorphismFromImageWithGivenImageObject
      6.11-14 AddImageObject
      6.11-15 AddImageEmbedding
      6.11-16 AddImageEmbeddingWithGivenImageObject
      6.11-17 AddCoastrictionToImage
      6.11-18 AddCoastrictionToImageWithGivenImageObject
      6.11-19 AddUniversalMorphismFromImage
      6.11-20 AddUniversalMorphismFromImageWithGivenImageObject
    6.12 [33X[0;0YCoimage[133X
      6.12-1 MorphismFromCoimageToImage
      6.12-2 MorphismFromCoimageToImageWithGivenObjects
      6.12-3 AddMorphismFromCoimageToImageWithGivenObjects
      6.12-4 InverseMorphismFromCoimageToImage
      6.12-5 InverseMorphismFromCoimageToImageWithGivenObjects
      6.12-6 AddInverseMorphismFromCoimageToImageWithGivenObjects
      6.12-7 IsomorphismFromCoimageToCokernelOfKernel
      6.12-8 AddIsomorphismFromCoimageToCokernelOfKernel
      6.12-9 IsomorphismFromCokernelOfKernelToCoimage
      6.12-10 AddIsomorphismFromCokernelOfKernelToCoimage
      6.12-11 Coimage
      6.12-12 CoimageProjection
      6.12-13 CoimageProjection
      6.12-14 CoimageProjectionWithGivenCoimage
      6.12-15 AstrictionToCoimage
      6.12-16 AstrictionToCoimage
      6.12-17 AstrictionToCoimageWithGivenCoimage
      6.12-18 UniversalMorphismIntoCoimage
      6.12-19 UniversalMorphismIntoCoimageWithGivenCoimage
      6.12-20 AddCoimage
      6.12-21 AddCoimageProjection
      6.12-22 AddCoimageProjectionWithGivenCoimage
      6.12-23 AddAstrictionToCoimage
      6.12-24 AddAstrictionToCoimageWithGivenCoimage
      6.12-25 AddUniversalMorphismIntoCoimage
      6.12-26 AddUniversalMorphismIntoCoimageWithGivenCoimage
    6.13 [33X[0;0YConvenience Methods[133X
      6.13-1 InjectionOfCofactor
      6.13-2 ProjectionInFactor
  7 [33X[0;0YTensor Product and Internal Hom[133X
    7.1 [33X[0;0YMonoidal Categories[133X
      7.1-1 TensorProductOnObjects
      7.1-2 AddTensorProductOnObjects
      7.1-3 TensorProductOnMorphisms
      7.1-4 TensorProductOnMorphismsWithGivenTensorProducts
      7.1-5 AddTensorProductOnMorphismsWithGivenTensorProducts
      7.1-6 AssociatorRightToLeft
      7.1-7 AssociatorRightToLeftWithGivenTensorProducts
      7.1-8 AddAssociatorRightToLeftWithGivenTensorProducts
      7.1-9 AssociatorLeftToRight
      7.1-10 AssociatorLeftToRightWithGivenTensorProducts
      7.1-11 AddAssociatorLeftToRightWithGivenTensorProducts
      7.1-12 TensorUnit
      7.1-13 AddTensorUnit
      7.1-14 LeftUnitor
      7.1-15 LeftUnitorWithGivenTensorProduct
      7.1-16 AddLeftUnitorWithGivenTensorProduct
      7.1-17 LeftUnitorInverse
      7.1-18 LeftUnitorInverseWithGivenTensorProduct
      7.1-19 AddLeftUnitorInverseWithGivenTensorProduct
      7.1-20 RightUnitor
      7.1-21 RightUnitorWithGivenTensorProduct
      7.1-22 AddRightUnitorWithGivenTensorProduct
      7.1-23 RightUnitorInverse
      7.1-24 RightUnitorInverseWithGivenTensorProduct
      7.1-25 AddRightUnitorInverseWithGivenTensorProduct
      7.1-26 LeftDistributivityExpanding
      7.1-27 LeftDistributivityExpandingWithGivenObjects
      7.1-28 AddLeftDistributivityExpandingWithGivenObjects
      7.1-29 LeftDistributivityFactoring
      7.1-30 LeftDistributivityFactoringWithGivenObjects
      7.1-31 AddLeftDistributivityFactoringWithGivenObjects
      7.1-32 RightDistributivityExpanding
      7.1-33 RightDistributivityExpandingWithGivenObjects
      7.1-34 AddRightDistributivityExpandingWithGivenObjects
      7.1-35 RightDistributivityFactoring
      7.1-36 RightDistributivityFactoringWithGivenObjects
      7.1-37 AddRightDistributivityFactoringWithGivenObjects
    7.2 [33X[0;0YBraided Monoidal Categories[133X
      7.2-1 Braiding
      7.2-2 BraidingWithGivenTensorProducts
      7.2-3 AddBraidingWithGivenTensorProducts
      7.2-4 BraidingInverse
      7.2-5 BraidingInverseWithGivenTensorProducts
      7.2-6 AddBraidingInverseWithGivenTensorProducts
    7.3 [33X[0;0YSymmetric Monoidal Categories[133X
    7.4 [33X[0;0YSymmetric Closed Monoidal Categories[133X
      7.4-1 InternalHomOnObjects
      7.4-2 AddInternalHomOnObjects
      7.4-3 InternalHomOnMorphisms
      7.4-4 InternalHomOnMorphismsWithGivenInternalHoms
      7.4-5 AddInternalHomOnMorphismsWithGivenInternalHoms
      7.4-6 EvaluationMorphism
      7.4-7 EvaluationMorphismWithGivenSource
      7.4-8 AddEvaluationMorphismWithGivenSource
      7.4-9 CoevaluationMorphism
      7.4-10 CoevaluationMorphismWithGivenRange
      7.4-11 AddCoevaluationMorphismWithGivenRange
      7.4-12 TensorProductToInternalHomAdjunctionMap
      7.4-13 AddTensorProductToInternalHomAdjunctionMap
      7.4-14 InternalHomToTensorProductAdjunctionMap
      7.4-15 AddInternalHomToTensorProductAdjunctionMap
      7.4-16 MonoidalPreComposeMorphism
      7.4-17 MonoidalPreComposeMorphismWithGivenObjects
      7.4-18 AddMonoidalPreComposeMorphismWithGivenObjects
      7.4-19 MonoidalPostComposeMorphism
      7.4-20 MonoidalPostComposeMorphismWithGivenObjects
      7.4-21 AddMonoidalPostComposeMorphismWithGivenObjects
      7.4-22 DualOnObjects
      7.4-23 AddDualOnObjects
      7.4-24 DualOnMorphisms
      7.4-25 DualOnMorphismsWithGivenDuals
      7.4-26 AddDualOnMorphismsWithGivenDuals
      7.4-27 EvaluationForDual
      7.4-28 EvaluationForDualWithGivenTensorProduct
      7.4-29 AddEvaluationForDualWithGivenTensorProduct
      7.4-30 CoevaluationForDual
      7.4-31 CoevaluationForDualWithGivenTensorProduct
      7.4-32 AddCoevaluationForDualWithGivenTensorProduct
      7.4-33 MorphismToBidual
      7.4-34 MorphismToBidualWithGivenBidual
      7.4-35 AddMorphismToBidualWithGivenBidual
      7.4-36 TensorProductInternalHomCompatibilityMorphism
      7.4-37 TensorProductInternalHomCompatibilityMorphismWithGivenObjects
      7.4-38 AddTensorProductInternalHomCompatibilityMorphismWithGivenObjects
      7.4-39 TensorProductDualityCompatibilityMorphism
      7.4-40 TensorProductDualityCompatibilityMorphismWithGivenObjects
      7.4-41 AddTensorProductDualityCompatibilityMorphismWithGivenObjects
      7.4-42 MorphismFromTensorProductToInternalHom
      7.4-43 MorphismFromTensorProductToInternalHomWithGivenObjects
      7.4-44 AddMorphismFromTensorProductToInternalHomWithGivenObjects
      7.4-45 IsomorphismFromTensorProductToInternalHom
      7.4-46 AddIsomorphismFromTensorProductToInternalHom
      7.4-47 MorphismFromInternalHomToTensorProduct
      7.4-48 MorphismFromInternalHomToTensorProductWithGivenObjects
      7.4-49 AddMorphismFromInternalHomToTensorProductWithGivenObjects
      7.4-50 IsomorphismFromInternalHomToTensorProduct
      7.4-51 AddIsomorphismFromInternalHomToTensorProduct
      7.4-52 TraceMap
      7.4-53 AddTraceMap
      7.4-54 RankMorphism
      7.4-55 AddRankMorphism
      7.4-56 IsomorphismFromDualToInternalHom
      7.4-57 AddIsomorphismFromDualToInternalHom
      7.4-58 IsomorphismFromInternalHomToDual
      7.4-59 AddIsomorphismFromInternalHomToDual
      7.4-60 UniversalPropertyOfDual
      7.4-61 AddUniversalPropertyOfDual
      7.4-62 LambdaIntroduction
      7.4-63 AddLambdaIntroduction
      7.4-64 LambdaElimination
      7.4-65 AddLambdaElimination
      7.4-66 IsomorphismFromObjectToInternalHom
      7.4-67 IsomorphismFromObjectToInternalHomWithGivenInternalHom
      7.4-68 AddIsomorphismFromObjectToInternalHomWithGivenInternalHom
      7.4-69 IsomorphismFromInternalHomToObject
      7.4-70 IsomorphismFromInternalHomToObjectWithGivenInternalHom
      7.4-71 AddIsomorphismFromInternalHomToObjectWithGivenInternalHom
    7.5 [33X[0;0YRigid Symmetric Closed Monoidal Categories[133X
      7.5-1 TensorProductInternalHomCompatibilityMorphismInverse
      7.5-2 TensorProductInternalHomCompatibilityMorphismInverseWithGivenObjects
      7.5-3 AddTensorProductInternalHomCompatibilityMorphismInverseWithGivenObjects
      7.5-4 MorphismFromBidual
      7.5-5 MorphismFromBidualWithGivenBidual
      7.5-6 AddMorphismFromBidualWithGivenBidual
  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 DerivationFunctionsWithExtraFilters
      8.2-6 CategoryFilter
      8.2-7 IsApplicableToCategory
      8.2-8 TargetOperation
      8.2-9 UsedOperations
      8.2-10 UsedOperationMultiples
      8.2-11 UsedOperationsWithMultiples
      8.2-12 InstallDerivationForCategory
      8.2-13 DerivationResultWeight
    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 AddDerivationPair
      8.3-9 AddDerivationPair
      8.3-10 AddDerivationPair
      8.3-11 AddDerivationPair
      8.3-12 AddDerivationToCAP
      8.3-13 AddDerivationPairToCAP
      8.3-14 AddWithGivenDerivationPairToCAP
      8.3-15 Operations
      8.3-16 DerivationsUsingOperation
      8.3-17 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 AddPrimitiveOperation
      8.4-11 PrintDerivationTree
      8.4-12 PrintTree
      8.4-13 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;0YAdd Functions[133X
    9.1 [33X[0;0YFunctions Installed by Add[133X
    9.2 [33X[0;0YAdd Method[133X
    9.3 [33X[0;0YInstallAdd Function[133X
    9.4 [33X[0;0YInstall All Adds[133X
  10 [33X[0;0YTechnical Details[133X
    10.1 [33X[0;0YThe Category Cat[133X
      10.1-1 ObjectCache
      10.1-2 MorphismCache
    10.2 [33X[0;0YInstall Functions for IsWellDefined[133X
      10.2-1 InstallMethodWithToDoForIsWellDefined
      10.2-2 InstallSetWithToDoForIsWellDefined
      10.2-3 DeclareAttributeWithToDoForIsWellDefined
      10.2-4 DeclareFamilyProperty
      10.2-5 CAP_INTERNAL_REPLACE_STRINGS_WITH_FILTERS
      10.2-6 CAP_INTERNAL_MERGE_FILTER_LISTS
      10.2-7 CAP_INTERNAL_RETURN_OPTION_OR_DEFAULT
      10.2-8 CAP_INTERNAL_FIND_APPEARANCE_OF_SYMBOL_IN_FUNCTION
      10.2-9 CAP_INTERNAL_MERGE_PRECONDITIONS_LIST
    10.3 [33X[0;0YUniversal Objects[133X
      10.3-1 WasCreatedAsKernelObject
      10.3-2 WasCreatedAsCokernelObject
      10.3-3 WasCreatedAsZeroObject
      10.3-4 WasCreatedAsTerminalObject
      10.3-5 WasCreatedAsInitialObject
      10.3-6 WasCreatedAsDirectSum
      10.3-7 WasCreatedAsCoproduct
      10.3-8 WasCreatedAsDirectProduct
      10.3-9 WasCreatedAsFiberProduct
      10.3-10 WasCreatedAsPushout
      10.3-11 WasCreatedAsImageObject
  11 [33X[0;0YExamples and Tests[133X
    11.1 [33X[0;0YSpectral Sequences[133X
    11.2 [33X[0;0YMonoidal Categories[133X
    11.3 [33X[0;0YGeneralized Morphisms Category[133X
    11.4 [33X[0;0YIsWellDefined[133X
    11.5 [33X[0;0YKernel[133X
    11.6 [33X[0;0YFiberProduct[133X
  
  
  [32X
