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CartesianCategories

Cartesian and cocartesian categories and various subdoctrines

2026.05-01

7 May 2026

Mohamed Barakat
Email: mohamed.barakat@uni-siegen.de
Homepage: https://mohamed-barakat.github.io
Address:
Walter-Flex-Str. 3
57068 Siegen
Germany

Fabian Zickgraf
Email: f.zickgraf@dashdos.com
Homepage: https://github.com/zickgraf/
Address:
Walter-Flex-Str. 3
57068 Siegen
Germany

Tom Kuhmichel
Email: tom.kuhmichel@student.uni-siegen.de
Homepage: https://github.com/TKuh
Address:
Walter-Flex-Str. 3
57068 Siegen
Germany

Contents

1 Cartesian Categories
 1.1 Cartesian Categories

  1.1-1 CartesianBraiding
  1.1-2 CartesianBraidingWithGivenDirectProducts
  1.1-3 CartesianBraidingInverse
  1.1-4 CartesianBraidingInverseWithGivenDirectProducts
  1.1-5 DirectProductOnMorphisms
  1.1-6 DirectProductOnMorphismsWithGivenDirectProducts
  1.1-7 DirectProductOnMorphismAndObject
  1.1-8 DirectProductOnMorphismAndObjectWithGivenDirectProducts
  1.1-9 DirectProductOnObjectAndMorphism
  1.1-10 DirectProductOnObjectAndMorphismWithGivenDirectProducts
  1.1-11 CartesianAssociatorRightToLeft
  1.1-12 CartesianAssociatorRightToLeftWithGivenDirectProducts
  1.1-13 CartesianAssociatorLeftToRight
  1.1-14 CartesianAssociatorLeftToRightWithGivenDirectProducts
  1.1-15 CartesianLeftUnitor
  1.1-16 CartesianLeftUnitorWithGivenDirectProduct
  1.1-17 CartesianLeftUnitorInverse
  1.1-18 CartesianLeftUnitorInverseWithGivenDirectProduct
  1.1-19 CartesianRightUnitor
  1.1-20 CartesianRightUnitorWithGivenDirectProduct
  1.1-21 CartesianRightUnitorInverse
  1.1-22 CartesianRightUnitorInverseWithGivenDirectProduct
  1.1-23 IsSymmetricMonoidalCategoryStructureGivenByDirectProduct
  1.1-24 CartesianDiagonal
  1.1-25 CartesianDiagonalWithGivenCartesianPower
  1.1-26 SetTensorProductToDirectProduct
  1.1-27 LeftCartesianDistributivityExpanding
  1.1-28 LeftCartesianDistributivityExpandingWithGivenObjects
  1.1-29 LeftCartesianDistributivityFactoring
  1.1-30 LeftCartesianDistributivityFactoringWithGivenObjects
  1.1-31 RightCartesianDistributivityExpanding
  1.1-32 RightCartesianDistributivityExpandingWithGivenObjects
  1.1-33 RightCartesianDistributivityFactoring
  1.1-34 RightCartesianDistributivityFactoringWithGivenObjects
 1.2 Cartesian Closed Categories

  1.2-1 ExponentialOnObjects
  1.2-2 ExponentialOnMorphisms
  1.2-3 ExponentialOnMorphismsWithGivenExponentials
  1.2-4 CartesianRightEvaluationMorphism
  1.2-5 CartesianRightEvaluationMorphismWithGivenSource
  1.2-6 CartesianRightCoevaluationMorphism
  1.2-7 CartesianRightCoevaluationMorphismWithGivenRange
  1.2-8 DirectProductToExponentialRightAdjunctMorphism
  1.2-9 DirectProductToExponentialRightAdjunctMorphismWithGivenExponential
  1.2-10 DirectProductToExponentialRightAdjunctionIsomorphism
  1.2-11 DirectProductToExponentialRightAdjunctionIsomorphismWithGivenObjects
  1.2-12 ExponentialToDirectProductRightAdjunctMorphism
  1.2-13 ExponentialToDirectProductRightAdjunctMorphismWithGivenDirectProduct
  1.2-14 ExponentialToDirectProductRightAdjunctionIsomorphism
  1.2-15 ExponentialToDirectProductRightAdjunctionIsomorphismWithGivenObjects
  1.2-16 CartesianLeftEvaluationMorphism
  1.2-17 CartesianLeftEvaluationMorphismWithGivenSource
  1.2-18 CartesianLeftCoevaluationMorphism
  1.2-19 CartesianLeftCoevaluationMorphismWithGivenRange
  1.2-20 DirectProductToExponentialLeftAdjunctMorphism
  1.2-21 DirectProductToExponentialLeftAdjunctMorphismWithGivenExponential
  1.2-22 DirectProductToExponentialLeftAdjunctionIsomorphism
  1.2-23 DirectProductToExponentialLeftAdjunctionIsomorphismWithGivenObjects
  1.2-24 ExponentialToDirectProductLeftAdjunctMorphism
  1.2-25 ExponentialToDirectProductLeftAdjunctMorphismWithGivenDirectProduct
  1.2-26 ExponentialToDirectProductLeftAdjunctionIsomorphism
  1.2-27 ExponentialToDirectProductLeftAdjunctionIsomorphismWithGivenObjects
  1.2-28 CartesianPreComposeMorphism
  1.2-29 CartesianPreComposeMorphismWithGivenObjects
  1.2-30 CartesianPostComposeMorphism
  1.2-31 CartesianPostComposeMorphismWithGivenObjects
  1.2-32 CartesianDualOnObjects
  1.2-33 CartesianDualOnMorphisms
  1.2-34 CartesianDualOnMorphismsWithGivenCartesianDuals
  1.2-35 CartesianEvaluationForCartesianDual
  1.2-36 CartesianEvaluationForCartesianDualWithGivenDirectProduct
  1.2-37 MorphismToCartesianBidual
  1.2-38 MorphismToCartesianBidualWithGivenCartesianBidual
  1.2-39 DirectProductExponentialCompatibilityMorphism
  1.2-40 DirectProductExponentialCompatibilityMorphismWithGivenObjects
  1.2-41 DirectProductCartesianDualityCompatibilityMorphism
  1.2-42 DirectProductCartesianDualityCompatibilityMorphismWithGivenObjects
  1.2-43 MorphismFromDirectProductToExponential
  1.2-44 MorphismFromDirectProductToExponentialWithGivenObjects
  1.2-45 IsomorphismFromCartesianDualObjectToExponentialIntoTerminalObject
  1.2-46 IsomorphismFromExponentialIntoTerminalObjectToCartesianDualObject
  1.2-47 UniversalPropertyOfCartesianDual
  1.2-48 CartesianLambdaIntroduction
  1.2-49 CartesianLambdaElimination
  1.2-50 IsomorphismFromObjectToExponential
  1.2-51 IsomorphismFromObjectToExponentialWithGivenExponential
  1.2-52 IsomorphismFromExponentialToObject
  1.2-53 IsomorphismFromExponentialToObjectWithGivenExponential
 1.3 Convenience Methods

  1.3-1 Exponential
 1.4 Add-methods

  1.4-1 AddCartesianBraiding
  1.4-2 AddCartesianBraidingInverse
  1.4-3 AddCartesianBraidingInverseWithGivenDirectProducts
  1.4-4 AddCartesianBraidingWithGivenDirectProducts
  1.4-5 AddCartesianAssociatorLeftToRight
  1.4-6 AddCartesianAssociatorLeftToRightWithGivenDirectProducts
  1.4-7 AddCartesianAssociatorRightToLeft
  1.4-8 AddCartesianAssociatorRightToLeftWithGivenDirectProducts
  1.4-9 AddCartesianDiagonal
  1.4-10 AddCartesianDiagonalWithGivenCartesianPower
  1.4-11 AddCartesianLeftUnitor
  1.4-12 AddCartesianLeftUnitorInverse
  1.4-13 AddCartesianLeftUnitorInverseWithGivenDirectProduct
  1.4-14 AddCartesianLeftUnitorWithGivenDirectProduct
  1.4-15 AddCartesianRightUnitor
  1.4-16 AddCartesianRightUnitorInverse
  1.4-17 AddCartesianRightUnitorInverseWithGivenDirectProduct
  1.4-18 AddCartesianRightUnitorWithGivenDirectProduct
  1.4-19 AddDirectProductOnMorphismAndObject
  1.4-20 AddDirectProductOnMorphismAndObjectWithGivenDirectProducts
  1.4-21 AddDirectProductOnMorphisms
  1.4-22 AddDirectProductOnMorphismsWithGivenDirectProducts
  1.4-23 AddDirectProductOnObjectAndMorphism
  1.4-24 AddDirectProductOnObjectAndMorphismWithGivenDirectProducts
  1.4-25 AddCartesianDualOnMorphisms
  1.4-26 AddCartesianDualOnMorphismsWithGivenCartesianDuals
  1.4-27 AddCartesianDualOnObjects
  1.4-28 AddCartesianEvaluationForCartesianDual
  1.4-29 AddCartesianEvaluationForCartesianDualWithGivenDirectProduct
  1.4-30 AddCartesianLambdaElimination
  1.4-31 AddCartesianLambdaIntroduction
  1.4-32 AddCartesianLeftCoevaluationMorphism
  1.4-33 AddCartesianLeftCoevaluationMorphismWithGivenRange
  1.4-34 AddCartesianLeftEvaluationMorphism
  1.4-35 AddCartesianLeftEvaluationMorphismWithGivenSource
  1.4-36 AddCartesianPostComposeMorphism
  1.4-37 AddCartesianPostComposeMorphismWithGivenObjects
  1.4-38 AddCartesianPreComposeMorphism
  1.4-39 AddCartesianPreComposeMorphismWithGivenObjects
  1.4-40 AddCartesianRightCoevaluationMorphism
  1.4-41 AddCartesianRightCoevaluationMorphismWithGivenRange
  1.4-42 AddCartesianRightEvaluationMorphism
  1.4-43 AddCartesianRightEvaluationMorphismWithGivenSource
  1.4-44 AddDirectProductCartesianDualityCompatibilityMorphism
  1.4-45 AddDirectProductCartesianDualityCompatibilityMorphismWithGivenObjects
  1.4-46 AddDirectProductExponentialCompatibilityMorphism
  1.4-47 AddDirectProductExponentialCompatibilityMorphismWithGivenObjects
  1.4-48 AddDirectProductToExponentialLeftAdjunctMorphism
  1.4-49 AddDirectProductToExponentialLeftAdjunctMorphismWithGivenExponential
  1.4-50 AddDirectProductToExponentialLeftAdjunctionIsomorphism
  1.4-51 AddDirectProductToExponentialLeftAdjunctionIsomorphismWithGivenObjects
  1.4-52 AddDirectProductToExponentialRightAdjunctMorphism
  1.4-53 AddDirectProductToExponentialRightAdjunctMorphismWithGivenExponential
  1.4-54 AddDirectProductToExponentialRightAdjunctionIsomorphism
  1.4-55 AddDirectProductToExponentialRightAdjunctionIsomorphismWithGivenObjects
  1.4-56 AddExponentialOnMorphisms
  1.4-57 AddExponentialOnMorphismsWithGivenExponentials
  1.4-58 AddExponentialOnObjects
  1.4-59 AddExponentialToDirectProductLeftAdjunctMorphism
  1.4-60 AddExponentialToDirectProductLeftAdjunctMorphismWithGivenDirectProduct
  1.4-61 AddExponentialToDirectProductLeftAdjunctionIsomorphism
  1.4-62 AddExponentialToDirectProductLeftAdjunctionIsomorphismWithGivenObjects
  1.4-63 AddExponentialToDirectProductRightAdjunctMorphism
  1.4-64 AddExponentialToDirectProductRightAdjunctMorphismWithGivenDirectProduct
  1.4-65 AddExponentialToDirectProductRightAdjunctionIsomorphism
  1.4-66 AddExponentialToDirectProductRightAdjunctionIsomorphismWithGivenObjects
  1.4-67 AddIsomorphismFromCartesianDualObjectToExponentialIntoTerminalObject
  1.4-68 AddIsomorphismFromExponentialIntoTerminalObjectToCartesianDualObject
  1.4-69 AddIsomorphismFromExponentialToObject
  1.4-70 AddIsomorphismFromExponentialToObjectWithGivenExponential
  1.4-71 AddIsomorphismFromObjectToExponential
  1.4-72 AddIsomorphismFromObjectToExponentialWithGivenExponential
  1.4-73 AddMorphismFromDirectProductToExponential
  1.4-74 AddMorphismFromDirectProductToExponentialWithGivenObjects
  1.4-75 AddMorphismToCartesianBidual
  1.4-76 AddMorphismToCartesianBidualWithGivenCartesianBidual
  1.4-77 AddUniversalPropertyOfCartesianDual
  1.4-78 AddLeftCartesianDistributivityExpanding
  1.4-79 AddLeftCartesianDistributivityExpandingWithGivenObjects
  1.4-80 AddLeftCartesianDistributivityFactoring
  1.4-81 AddLeftCartesianDistributivityFactoringWithGivenObjects
  1.4-82 AddRightCartesianDistributivityExpanding
  1.4-83 AddRightCartesianDistributivityExpandingWithGivenObjects
  1.4-84 AddRightCartesianDistributivityFactoring
  1.4-85 AddRightCartesianDistributivityFactoringWithGivenObjects
2 Cocartesian Categories
 2.1 Cocartesian Categories

  2.1-1 CocartesianBraiding
  2.1-2 CocartesianBraidingWithGivenCoproducts
  2.1-3 CocartesianBraidingInverse
  2.1-4 CocartesianBraidingInverseWithGivenCoproducts
  2.1-5 CoproductOnMorphisms
  2.1-6 CoproductOnMorphismsWithGivenCoproducts
  2.1-7 CoproductOnMorphismAndObject
  2.1-8 CoproductOnMorphismAndObjectWithGivenCoproducts
  2.1-9 CoproductOnObjectAndMorphism
  2.1-10 CoproductOnObjectAndMorphismWithGivenCoproducts
  2.1-11 CocartesianAssociatorRightToLeft
  2.1-12 CocartesianAssociatorRightToLeftWithGivenCoproducts
  2.1-13 CocartesianAssociatorLeftToRight
  2.1-14 CocartesianAssociatorLeftToRightWithGivenCoproducts
  2.1-15 CocartesianLeftUnitor
  2.1-16 CocartesianLeftUnitorWithGivenCoproduct
  2.1-17 CocartesianLeftUnitorInverse
  2.1-18 CocartesianLeftUnitorInverseWithGivenCoproduct
  2.1-19 CocartesianRightUnitor
  2.1-20 CocartesianRightUnitorWithGivenCoproduct
  2.1-21 CocartesianRightUnitorInverse
  2.1-22 CocartesianRightUnitorInverseWithGivenCoproduct
  2.1-23 IsSymmetricMonoidalCategoryStructureGivenByCoproduct
  2.1-24 CocartesianCodiagonal
  2.1-25 CocartesianCodiagonalWithGivenCocartesianMultiple
  2.1-26 SetTensorProductToCoproduct
  2.1-27 LeftCocartesianCodistributivityExpanding
  2.1-28 LeftCocartesianCodistributivityExpandingWithGivenObjects
  2.1-29 LeftCocartesianCodistributivityFactoring
  2.1-30 LeftCocartesianCodistributivityFactoringWithGivenObjects
  2.1-31 RightCocartesianCodistributivityExpanding
  2.1-32 RightCocartesianCodistributivityExpandingWithGivenObjects
  2.1-33 RightCocartesianCodistributivityFactoring
  2.1-34 RightCocartesianCodistributivityFactoringWithGivenObjects
 2.2 Cocartesian Coclosed Categories

  2.2-1 CoexponentialOnObjects
  2.2-2 CoexponentialOnMorphisms
  2.2-3 CoexponentialOnMorphismsWithGivenCoexponentials
  2.2-4 CocartesianRightEvaluationMorphism
  2.2-5 CocartesianRightEvaluationMorphismWithGivenRange
  2.2-6 CocartesianRightCoevaluationMorphism
  2.2-7 CocartesianRightCoevaluationMorphismWithGivenSource
  2.2-8 CoproductToCoexponentialRightAdjunctMorphism
  2.2-9 CoproductToCoexponentialRightAdjunctMorphismWithGivenCoexponential
  2.2-10 CoexponentialToCoproductRightAdjunctMorphism
  2.2-11 CoexponentialToCoproductRightAdjunctMorphismWithGivenCoproduct
  2.2-12 CocartesianLeftEvaluationMorphism
  2.2-13 CocartesianLeftEvaluationMorphismWithGivenRange
  2.2-14 CocartesianLeftCoevaluationMorphism
  2.2-15 CocartesianLeftCoevaluationMorphismWithGivenSource
  2.2-16 CoproductToCoexponentialLeftAdjunctMorphism
  2.2-17 CoproductToCoexponentialLeftAdjunctMorphismWithGivenCoexponential
  2.2-18 CoexponentialToCoproductLeftAdjunctMorphism
  2.2-19 CoexponentialToCoproductLeftAdjunctMorphismWithGivenCoproduct
  2.2-20 CocartesianPreCoComposeMorphism
  2.2-21 CocartesianPreCoComposeMorphismWithGivenObjects
  2.2-22 CocartesianPostCoComposeMorphism
  2.2-23 CocartesianPostCoComposeMorphismWithGivenObjects
  2.2-24 CocartesianDualOnObjects
  2.2-25 CocartesianDualOnMorphisms
  2.2-26 CocartesianDualOnMorphismsWithGivenCocartesianDuals
  2.2-27 CocartesianEvaluationForCocartesianDual
  2.2-28 CocartesianEvaluationForCocartesianDualWithGivenCoproduct
  2.2-29 MorphismFromCocartesianBidual
  2.2-30 MorphismFromCocartesianBidualWithGivenCocartesianBidual
  2.2-31 CoexponentialCoproductCompatibilityMorphism
  2.2-32 CoexponentialCoproductCompatibilityMorphismWithGivenObjects
  2.2-33 CocartesianDualityCoproductCompatibilityMorphism
  2.2-34 CocartesianDualityCoproductCompatibilityMorphismWithGivenObjects
  2.2-35 MorphismFromCoexponentialToCoproduct
  2.2-36 MorphismFromCoexponentialToCoproductWithGivenObjects
  2.2-37 IsomorphismFromCocartesianDualObjectToCoexponentialFromInitialObject
  2.2-38 IsomorphismFromCoexponentialFromInitialObjectToCocartesianDualObject
  2.2-39 UniversalPropertyOfCocartesianDual
  2.2-40 CocartesianLambdaIntroduction
  2.2-41 CocartesianLambdaElimination
  2.2-42 IsomorphismFromObjectToCoexponential
  2.2-43 IsomorphismFromObjectToCoexponentialWithGivenCoexponential
  2.2-44 IsomorphismFromCoexponentialToObject
  2.2-45 IsomorphismFromCoexponentialToObjectWithGivenCoexponential
 2.3 Convenience Methods

  2.3-1 Coexponential
 2.4 Add-methods

  2.4-1 AddCocartesianBraiding
  2.4-2 AddCocartesianBraidingInverse
  2.4-3 AddCocartesianBraidingInverseWithGivenCoproducts
  2.4-4 AddCocartesianBraidingWithGivenCoproducts
  2.4-5 AddCocartesianAssociatorLeftToRight
  2.4-6 AddCocartesianAssociatorLeftToRightWithGivenCoproducts
  2.4-7 AddCocartesianAssociatorRightToLeft
  2.4-8 AddCocartesianAssociatorRightToLeftWithGivenCoproducts
  2.4-9 AddCocartesianCodiagonal
  2.4-10 AddCocartesianCodiagonalWithGivenCocartesianMultiple
  2.4-11 AddCocartesianLeftUnitor
  2.4-12 AddCocartesianLeftUnitorInverse
  2.4-13 AddCocartesianLeftUnitorInverseWithGivenCoproduct
  2.4-14 AddCocartesianLeftUnitorWithGivenCoproduct
  2.4-15 AddCocartesianRightUnitor
  2.4-16 AddCocartesianRightUnitorInverse
  2.4-17 AddCocartesianRightUnitorInverseWithGivenCoproduct
  2.4-18 AddCocartesianRightUnitorWithGivenCoproduct
  2.4-19 AddCoproductOnMorphismAndObject
  2.4-20 AddCoproductOnMorphismAndObjectWithGivenCoproducts
  2.4-21 AddCoproductOnMorphisms
  2.4-22 AddCoproductOnMorphismsWithGivenCoproducts
  2.4-23 AddCoproductOnObjectAndMorphism
  2.4-24 AddCoproductOnObjectAndMorphismWithGivenCoproducts
  2.4-25 AddCocartesianDualOnMorphisms
  2.4-26 AddCocartesianDualOnMorphismsWithGivenCocartesianDuals
  2.4-27 AddCocartesianDualOnObjects
  2.4-28 AddCocartesianDualityCoproductCompatibilityMorphism
  2.4-29 AddCocartesianDualityCoproductCompatibilityMorphismWithGivenObjects
  2.4-30 AddCocartesianEvaluationForCocartesianDual
  2.4-31 AddCocartesianEvaluationForCocartesianDualWithGivenCoproduct
  2.4-32 AddCocartesianLambdaElimination
  2.4-33 AddCocartesianLambdaIntroduction
  2.4-34 AddCocartesianLeftCoevaluationMorphism
  2.4-35 AddCocartesianLeftCoevaluationMorphismWithGivenSource
  2.4-36 AddCocartesianLeftEvaluationMorphism
  2.4-37 AddCocartesianLeftEvaluationMorphismWithGivenRange
  2.4-38 AddCocartesianPostCoComposeMorphism
  2.4-39 AddCocartesianPostCoComposeMorphismWithGivenObjects
  2.4-40 AddCocartesianPreCoComposeMorphism
  2.4-41 AddCocartesianPreCoComposeMorphismWithGivenObjects
  2.4-42 AddCocartesianRightCoevaluationMorphism
  2.4-43 AddCocartesianRightCoevaluationMorphismWithGivenSource
  2.4-44 AddCocartesianRightEvaluationMorphism
  2.4-45 AddCocartesianRightEvaluationMorphismWithGivenRange
  2.4-46 AddCoexponentialCoproductCompatibilityMorphism
  2.4-47 AddCoexponentialCoproductCompatibilityMorphismWithGivenObjects
  2.4-48 AddCoexponentialOnMorphisms
  2.4-49 AddCoexponentialOnMorphismsWithGivenCoexponentials
  2.4-50 AddCoexponentialOnObjects
  2.4-51 AddCoexponentialToCoproductLeftAdjunctMorphism
  2.4-52 AddCoexponentialToCoproductLeftAdjunctMorphismWithGivenCoproduct
  2.4-53 AddCoexponentialToCoproductRightAdjunctMorphism
  2.4-54 AddCoexponentialToCoproductRightAdjunctMorphismWithGivenCoproduct
  2.4-55 AddCoproductToCoexponentialLeftAdjunctMorphism
  2.4-56 AddCoproductToCoexponentialLeftAdjunctMorphismWithGivenCoexponential
  2.4-57 AddCoproductToCoexponentialRightAdjunctMorphism
  2.4-58 AddCoproductToCoexponentialRightAdjunctMorphismWithGivenCoexponential
  2.4-59 AddIsomorphismFromCocartesianDualObjectToCoexponentialFromInitialObject
  2.4-60 AddIsomorphismFromCoexponentialFromInitialObjectToCocartesianDualObject
  2.4-61 AddIsomorphismFromCoexponentialToObject
  2.4-62 AddIsomorphismFromCoexponentialToObjectWithGivenCoexponential
  2.4-63 AddIsomorphismFromObjectToCoexponential
  2.4-64 AddIsomorphismFromObjectToCoexponentialWithGivenCoexponential
  2.4-65 AddMorphismFromCocartesianBidual
  2.4-66 AddMorphismFromCocartesianBidualWithGivenCocartesianBidual
  2.4-67 AddMorphismFromCoexponentialToCoproduct
  2.4-68 AddMorphismFromCoexponentialToCoproductWithGivenObjects
  2.4-69 AddUniversalPropertyOfCocartesianDual
  2.4-70 AddLeftCocartesianCodistributivityExpanding
  2.4-71 AddLeftCocartesianCodistributivityExpandingWithGivenObjects
  2.4-72 AddLeftCocartesianCodistributivityFactoring
  2.4-73 AddLeftCocartesianCodistributivityFactoringWithGivenObjects
  2.4-74 AddRightCocartesianCodistributivityExpanding
  2.4-75 AddRightCocartesianCodistributivityExpandingWithGivenObjects
  2.4-76 AddRightCocartesianCodistributivityFactoring
  2.4-77 AddRightCocartesianCodistributivityFactoringWithGivenObjects
3 Examples and Tests
 3.1 Test functions

  3.1-1 TestCartesianBraidingForInvertibility
  3.1-2 TestCartesianBraidingCompatibility
  3.1-3 TestCartesianBraidingCompatibilityForAllTriplesInList
  3.1-4 BraidedCartesianCategoriesTest
  3.1-5 TestCocartesianBraidingForInvertibility
  3.1-6 TestCocartesianBraidingCompatibility
  3.1-7 TestCocartesianBraidingCompatibilityForAllTriplesInList
  3.1-8 BraidedCocartesianCategoriesTest
  3.1-9 TestCartesianUnitorsForInvertibility
  3.1-10 TestCartesianAssociatorForInvertibility
  3.1-11 TestCartesianTriangleIdentity
  3.1-12 TestCartesianTriangleIdentityForAllPairsInList
  3.1-13 TestCartesianPentagonIdentity
  3.1-14 TestCartesianPentagonIdentityUsingWithGivenOperations
  3.1-15 TestCartesianPentagonIdentityForAllQuadruplesInList
  3.1-16 CartesianCategoriesTest
  3.1-17 CartesianClosedCategoriesTest
  3.1-18 TestCocartesianUnitorsForInvertibility
  3.1-19 TestCocartesianAssociatorForInvertibility
  3.1-20 TestCocartesianTriangleIdentity
  3.1-21 TestCocartesianTriangleIdentityForAllPairsInList
  3.1-22 TestCocartesianPentagonIdentity
  3.1-23 TestCocartesianPentagonIdentityUsingWithGivenOperations
  3.1-24 TestCocartesianPentagonIdentityForAllQuadruplesInList
  3.1-25 CocartesianCategoriesTest
  3.1-26 CocartesianCoclosedCategoriesTest
  3.1-27 CodistributiveCocartesianCategoriesTest
  3.1-28 DistributiveCartesianCategoriesTest
 3.2 InfoOfInstalledOperationsOfCategory
4 The initial category
 4.1 Constructor

  4.1-1 InitialCategory
 4.2 GAP Categories

  4.2-1 IsInitialCapCategory
  4.2-2 IsObjectInInitialCapCategory
  4.2-3 IsMorphismInInitialCapCategory
5 Legacy Operations and Synonyms
 5.1 Legacy operations

  5.1-1 CocartesianCoevaluationMorphism
  5.1-2 CocartesianCoevaluationMorphismWithGivenSource
  5.1-3 CocartesianEvaluationMorphism
  5.1-4 CocartesianEvaluationMorphismWithGivenRange
  5.1-5 CartesianCoevaluationMorphism
  5.1-6 CartesianCoevaluationMorphismWithGivenRange
 5.2 Synonyms for legacy operations

  5.2-1 CartesianEvaluationMorphism
  5.2-2 CartesianEvaluationMorphismWithGivenSource
  5.2-3 CoexponentialToCoproductAdjunctionMap
  5.2-4 CoexponentialToCoproductAdjunctionMapWithGivenCoproduct
  5.2-5 ExponentialToDirectProductAdjunctionMap
  5.2-6 ExponentialToDirectProductAdjunctionMapWithGivenDirectProduct
  5.2-7 CoproductToCoexponentialAdjunctionMap
  5.2-8 CoproductToCoexponentialAdjunctionMapWithGivenCoexponential
  5.2-9 DirectProductToExponentialAdjunctionMap
  5.2-10 DirectProductToExponentialAdjunctionMapWithGivenExponential
  5.2-11 AddCartesianEvaluationMorphism
  5.2-12 AddCartesianEvaluationMorphismWithGivenSource
  5.2-13 AddCoexponentialToCoproductAdjunctionMap
  5.2-14 AddCoexponentialToCoproductAdjunctionMapWithGivenCoproduct
  5.2-15 AddExponentialToDirectProductAdjunctionMap
  5.2-16 AddExponentialToDirectProductAdjunctionMapWithGivenDirectProduct
  5.2-17 AddCoproductToCoexponentialAdjunctionMap
  5.2-18 AddCoproductToCoexponentialAdjunctionMapWithGivenCoexponential
  5.2-19 AddDirectProductToExponentialAdjunctionMap
  5.2-20 AddDirectProductToExponentialAdjunctionMapWithGivenExponential
  5.2-21 CoexponentialToCoproductLeftAdjunctionMap
  5.2-22 CoexponentialToCoproductLeftAdjunctionMapWithGivenCoproduct
  5.2-23 ExponentialToDirectProductLeftAdjunctionMap
  5.2-24 ExponentialToDirectProductLeftAdjunctionMapWithGivenDirectProduct
  5.2-25 CoproductToCoexponentialLeftAdjunctionMap
  5.2-26 CoproductToCoexponentialLeftAdjunctionMapWithGivenCoexponential
  5.2-27 DirectProductToExponentialLeftAdjunctionMap
  5.2-28 DirectProductToExponentialLeftAdjunctionMapWithGivenExponential
  5.2-29 AddCoexponentialToCoproductLeftAdjunctionMap
  5.2-30 AddCoexponentialToCoproductLeftAdjunctionMapWithGivenCoproduct
  5.2-31 AddExponentialToDirectProductLeftAdjunctionMap
  5.2-32 AddExponentialToDirectProductLeftAdjunctionMapWithGivenDirectProduct
  5.2-33 AddCoproductToCoexponentialLeftAdjunctionMap
  5.2-34 AddCoproductToCoexponentialLeftAdjunctionMapWithGivenCoexponential
  5.2-35 AddDirectProductToExponentialLeftAdjunctionMap
  5.2-36 AddDirectProductToExponentialLeftAdjunctionMapWithGivenExponential
6 CartesianCategories automatic generated documentation
 6.1 CartesianCategories automatic generated documentation of properties

  6.1-1 IsBicartesianCategory
  6.1-2 IsFiniteCompleteCategory
  6.1-3 IsFiniteCocompleteCategory
  6.1-4 IsFiniteBicompleteCategory
  6.1-5 IsCartesianCategory
  6.1-6 IsStrictCartesianCategory
  6.1-7 IsCartesianClosedCategory
  6.1-8 IsBicartesianClosedCategory
  6.1-9 IsCocartesianCategory
  6.1-10 IsStrictCocartesianCategory
  6.1-11 IsCocartesianCoclosedCategory
  6.1-12 IsBicartesianCoclosedCategory
  6.1-13 IsCodistributiveCategory
  6.1-14 IsDistributiveCategory
  6.1-15 IsInitialCategory
Index

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