  
  
                              [1X MonoidalCategories [101X
  
  
                 [1X Monoidal and monoidal (co)closed categories [101X
  
  
                                   2024.06-01
  
  
                                  9 June 2024
  
  
                                Mohamed Barakat
  
                               Sebastian Gutsche
  
                                Sebastian Posur
  
                                 Tom Kuhmichel
  
                                Fabian Zickgraf
  
  
  
  Mohamed Barakat
      Email:    [7Xmailto:mohamed.barakat@uni-siegen.de[107X
      Homepage: [7Xhttp://algebra.mathematik.uni-siegen.de/barakat/[107X
      Address:  [33X[0;14YWalter-Flex-Str. 3[133X
                [33X[0;14Y57068 Siegen[133X
                [33X[0;14YGermany[133X
  
  
  Sebastian Gutsche
      Email:    [7Xmailto:gutsche@mathematik.uni-siegen.de[107X
      Homepage: [7Xhttp://algebra.mathematik.uni-siegen.de/gutsche/[107X
      Address:  [33X[0;14YDepartment Mathematik[133X
                [33X[0;14YUniversität Siegen[133X
                [33X[0;14YWalter-Flex-Straße 3[133X
                [33X[0;14Y57068 Siegen[133X
                [33X[0;14YGermany[133X
  
  
  Sebastian Posur
      Email:    [7Xmailto:sebastian.posur@uni-siegen.de[107X
      Homepage: [7Xhttp://algebra.mathematik.uni-siegen.de/posur/[107X
      Address:  [33X[0;14YDepartment Mathematik[133X
                [33X[0;14YUniversität Siegen[133X
                [33X[0;14YWalter-Flex-Straße 3[133X
                [33X[0;14Y57068 Siegen[133X
                [33X[0;14YGermany[133X
  
  
  Tom Kuhmichel
      Email:    [7Xmailto:tom.kuhmichel@student.uni-siegen.de[107X
      Homepage: [7Xhttps://github.com/TKuh[107X
      Address:  [33X[0;14YDepartment Mathematik[133X
                [33X[0;14YUniversität Siegen[133X
                [33X[0;14YWalter-Flex-Straße 3[133X
                [33X[0;14Y57068 Siegen[133X
                [33X[0;14YGermany[133X
  
  
  Fabian Zickgraf
      Email:    [7Xmailto:fabian.zickgraf@uni-siegen.de[107X
      Homepage: [7Xhttps://github.com/zickgraf/[107X
      Address:  [33X[0;14YWalter-Flex-Str. 3[133X
                [33X[0;14Y57068 Siegen[133X
                [33X[0;14YGermany[133X
  
  
  
  -------------------------------------------------------
  
  
  [1XContents (MonoidalCategories)[101X
  
  1 [33X[0;0YMonoidal Categories[133X
    1.1 [33X[0;0YMonoidal Categories[133X
      1.1-1 TensorProductOnMorphisms
      1.1-2 TensorProductOnMorphismsWithGivenTensorProducts
      1.1-3 AssociatorRightToLeft
      1.1-4 AssociatorRightToLeftWithGivenTensorProducts
      1.1-5 AssociatorLeftToRight
      1.1-6 AssociatorLeftToRightWithGivenTensorProducts
      1.1-7 LeftUnitor
      1.1-8 LeftUnitorWithGivenTensorProduct
      1.1-9 LeftUnitorInverse
      1.1-10 LeftUnitorInverseWithGivenTensorProduct
      1.1-11 RightUnitor
      1.1-12 RightUnitorWithGivenTensorProduct
      1.1-13 RightUnitorInverse
      1.1-14 RightUnitorInverseWithGivenTensorProduct
      1.1-15 TensorProductOnObjects
      1.1-16 AddTensorProductOnObjects
      1.1-17 TensorUnit
      1.1-18 AddTensorUnit
    1.2 [33X[0;0YAdditive Monoidal Categories[133X
      1.2-1 LeftDistributivityExpanding
      1.2-2 LeftDistributivityExpandingWithGivenObjects
      1.2-3 LeftDistributivityFactoring
      1.2-4 LeftDistributivityFactoringWithGivenObjects
      1.2-5 RightDistributivityExpanding
      1.2-6 RightDistributivityExpandingWithGivenObjects
      1.2-7 RightDistributivityFactoring
      1.2-8 RightDistributivityFactoringWithGivenObjects
    1.3 [33X[0;0YBraided Monoidal Categories[133X
      1.3-1 Braiding
      1.3-2 BraidingWithGivenTensorProducts
      1.3-3 BraidingInverse
      1.3-4 BraidingInverseWithGivenTensorProducts
    1.4 [33X[0;0YSymmetric Monoidal Categories[133X
    1.5 [33X[0;0YLeft Closed Monoidal Categories[133X
      1.5-1 LeftInternalHomOnObjects
      1.5-2 LeftInternalHomOnMorphisms
      1.5-3 LeftInternalHomOnMorphismsWithGivenLeftInternalHoms
      1.5-4 LeftClosedMonoidalEvaluationMorphism
      1.5-5 LeftClosedMonoidalEvaluationMorphismWithGivenSource
      1.5-6 LeftClosedMonoidalCoevaluationMorphism
      1.5-7 LeftClosedMonoidalCoevaluationMorphismWithGivenRange
      1.5-8 TensorProductToLeftInternalHomAdjunctMorphism
      1.5-9 TensorProductToLeftInternalHomAdjunctMorphismWithGivenLeftInternalHom
      1.5-10 LeftInternalHomToTensorProductAdjunctMorphism
      1.5-11 LeftInternalHomToTensorProductAdjunctMorphismWithGivenTensorProduct
      1.5-12 LeftClosedMonoidalPreComposeMorphism
      1.5-13 LeftClosedMonoidalPreComposeMorphismWithGivenObjects
      1.5-14 LeftClosedMonoidalPostComposeMorphism
      1.5-15 LeftClosedMonoidalPostComposeMorphismWithGivenObjects
      1.5-16 LeftDualOnObjects
      1.5-17 LeftDualOnMorphisms
      1.5-18 LeftDualOnMorphismsWithGivenLeftDuals
      1.5-19 LeftClosedMonoidalEvaluationForLeftDual
      1.5-20 LeftClosedMonoidalEvaluationForLeftDualWithGivenTensorProduct
      1.5-21 MorphismToLeftBidual
      1.5-22 MorphismToLeftBidualWithGivenLeftBidual
      1.5-23 TensorProductLeftInternalHomCompatibilityMorphism
      1.5-24 TensorProductLeftInternalHomCompatibilityMorphismWithGivenObjects
      1.5-25 TensorProductLeftDualityCompatibilityMorphism
      1.5-26 TensorProductLeftDualityCompatibilityMorphismWithGivenObjects
      1.5-27 MorphismFromTensorProductToLeftInternalHom
      1.5-28 MorphismFromTensorProductToLeftInternalHomWithGivenObjects
      1.5-29 IsomorphismFromLeftDualObjectToLeftInternalHomIntoTensorUnit
      1.5-30 IsomorphismFromLeftInternalHomIntoTensorUnitToLeftDualObject
      1.5-31 UniversalPropertyOfLeftDual
      1.5-32 LeftClosedMonoidalLambdaIntroduction
      1.5-33 LeftClosedMonoidalLambdaElimination
      1.5-34 IsomorphismFromObjectToLeftInternalHom
      1.5-35 IsomorphismFromObjectToLeftInternalHomWithGivenLeftInternalHom
      1.5-36 IsomorphismFromLeftInternalHomToObject
      1.5-37 IsomorphismFromLeftInternalHomToObjectWithGivenLeftInternalHom
    1.6 [33X[0;0YClosed Monoidal Categories[133X
      1.6-1 InternalHomOnObjects
      1.6-2 InternalHomOnMorphisms
      1.6-3 InternalHomOnMorphismsWithGivenInternalHoms
      1.6-4 ClosedMonoidalRightEvaluationMorphism
      1.6-5 ClosedMonoidalRightEvaluationMorphismWithGivenSource
      1.6-6 ClosedMonoidalRightCoevaluationMorphism
      1.6-7 ClosedMonoidalRightCoevaluationMorphismWithGivenRange
      1.6-8 TensorProductToInternalHomRightAdjunctMorphism
      1.6-9 TensorProductToInternalHomRightAdjunctMorphismWithGivenInternalHom
      1.6-10 TensorProductToInternalHomRightAdjunctionIsomorphism
      1.6-11 TensorProductToInternalHomRightAdjunctionIsomorphismWithGivenObjects
      1.6-12 InternalHomToTensorProductRightAdjunctMorphism
      1.6-13 InternalHomToTensorProductRightAdjunctMorphismWithGivenTensorProduct
      1.6-14 InternalHomToTensorProductRightAdjunctionIsomorphism
      1.6-15 InternalHomToTensorProductRightAdjunctionIsomorphismWithGivenObjects
      1.6-16 ClosedMonoidalLeftEvaluationMorphism
      1.6-17 ClosedMonoidalLeftEvaluationMorphismWithGivenSource
      1.6-18 ClosedMonoidalLeftCoevaluationMorphism
      1.6-19 ClosedMonoidalLeftCoevaluationMorphismWithGivenRange
      1.6-20 TensorProductToInternalHomLeftAdjunctMorphism
      1.6-21 TensorProductToInternalHomLeftAdjunctMorphismWithGivenInternalHom
      1.6-22 TensorProductToInternalHomLeftAdjunctionIsomorphism
      1.6-23 TensorProductToInternalHomLeftAdjunctionIsomorphismWithGivenObjects
      1.6-24 InternalHomToTensorProductLeftAdjunctMorphism
      1.6-25 InternalHomToTensorProductLeftAdjunctMorphismWithGivenTensorProduct
      1.6-26 InternalHomToTensorProductLeftAdjunctionIsomorphism
      1.6-27 InternalHomToTensorProductLeftAdjunctionIsomorphismWithGivenObjects
      1.6-28 MonoidalPreComposeMorphism
      1.6-29 MonoidalPreComposeMorphismWithGivenObjects
      1.6-30 MonoidalPostComposeMorphism
      1.6-31 MonoidalPostComposeMorphismWithGivenObjects
      1.6-32 DualOnObjects
      1.6-33 DualOnMorphisms
      1.6-34 DualOnMorphismsWithGivenDuals
      1.6-35 EvaluationForDual
      1.6-36 EvaluationForDualWithGivenTensorProduct
      1.6-37 MorphismToBidual
      1.6-38 MorphismToBidualWithGivenBidual
      1.6-39 TensorProductInternalHomCompatibilityMorphism
      1.6-40 TensorProductInternalHomCompatibilityMorphismWithGivenObjects
      1.6-41 TensorProductDualityCompatibilityMorphism
      1.6-42 TensorProductDualityCompatibilityMorphismWithGivenObjects
      1.6-43 MorphismFromTensorProductToInternalHom
      1.6-44 MorphismFromTensorProductToInternalHomWithGivenObjects
      1.6-45 IsomorphismFromDualObjectToInternalHomIntoTensorUnit
      1.6-46 IsomorphismFromInternalHomIntoTensorUnitToDualObject
      1.6-47 UniversalPropertyOfDual
      1.6-48 LambdaIntroduction
      1.6-49 LambdaElimination
      1.6-50 IsomorphismFromObjectToInternalHom
      1.6-51 IsomorphismFromObjectToInternalHomWithGivenInternalHom
      1.6-52 IsomorphismFromInternalHomToObject
      1.6-53 IsomorphismFromInternalHomToObjectWithGivenInternalHom
    1.7 [33X[0;0YLeft Coclosed Monoidal Categories[133X
      1.7-1 LeftInternalCoHomOnObjects
      1.7-2 LeftInternalCoHomOnMorphisms
      1.7-3 LeftInternalCoHomOnMorphismsWithGivenLeftInternalCoHoms
      1.7-4 LeftCoclosedMonoidalEvaluationMorphism
      1.7-5 LeftCoclosedMonoidalEvaluationMorphismWithGivenRange
      1.7-6 LeftCoclosedMonoidalCoevaluationMorphism
      1.7-7 LeftCoclosedMonoidalCoevaluationMorphismWithGivenSource
      1.7-8 TensorProductToLeftInternalCoHomAdjunctMorphism
      1.7-9 TensorProductToLeftInternalCoHomAdjunctMorphismWithGivenLeftInternalCoHom
      1.7-10 LeftInternalCoHomToTensorProductAdjunctMorphism
      1.7-11 LeftInternalCoHomToTensorProductAdjunctMorphismWithGivenTensorProduct
      1.7-12 LeftCoclosedMonoidalPreCoComposeMorphism
      1.7-13 LeftCoclosedMonoidalPreCoComposeMorphismWithGivenObjects
      1.7-14 LeftCoclosedMonoidalPostCoComposeMorphism
      1.7-15 LeftCoclosedMonoidalPostCoComposeMorphismWithGivenObjects
      1.7-16 LeftCoDualOnObjects
      1.7-17 LeftCoDualOnMorphisms
      1.7-18 LeftCoDualOnMorphismsWithGivenLeftCoDuals
      1.7-19 LeftCoclosedMonoidalEvaluationForLeftCoDual
      1.7-20 LeftCoclosedMonoidalEvaluationForLeftCoDualWithGivenTensorProduct
      1.7-21 MorphismFromLeftCoBidual
      1.7-22 MorphismFromLeftCoBidualWithGivenLeftCoBidual
      1.7-23 LeftInternalCoHomTensorProductCompatibilityMorphism
      1.7-24 LeftInternalCoHomTensorProductCompatibilityMorphismWithGivenObjects
      1.7-25 LeftCoDualityTensorProductCompatibilityMorphism
      1.7-26 LeftCoDualityTensorProductCompatibilityMorphismWithGivenObjects
      1.7-27 MorphismFromLeftInternalCoHomToTensorProduct
      1.7-28 MorphismFromLeftInternalCoHomToTensorProductWithGivenObjects
      1.7-29 IsomorphismFromLeftCoDualObjectToLeftInternalCoHomFromTensorUnit
      1.7-30 IsomorphismFromLeftInternalCoHomFromTensorUnitToLeftCoDualObject
      1.7-31 UniversalPropertyOfLeftCoDual
      1.7-32 LeftCoclosedMonoidalLambdaIntroduction
      1.7-33 LeftCoclosedMonoidalLambdaElimination
      1.7-34 IsomorphismFromObjectToLeftInternalCoHom
      1.7-35 IsomorphismFromObjectToLeftInternalCoHomWithGivenLeftInternalCoHom
      1.7-36 IsomorphismFromLeftInternalCoHomToObject
      1.7-37 IsomorphismFromLeftInternalCoHomToObjectWithGivenLeftInternalCoHom
    1.8 [33X[0;0YCoclosed Monoidal Categories[133X
      1.8-1 InternalCoHomOnObjects
      1.8-2 InternalCoHomOnMorphisms
      1.8-3 InternalCoHomOnMorphismsWithGivenInternalCoHoms
      1.8-4 CoclosedMonoidalRightEvaluationMorphism
      1.8-5 CoclosedMonoidalRightEvaluationMorphismWithGivenRange
      1.8-6 CoclosedMonoidalRightCoevaluationMorphism
      1.8-7 CoclosedMonoidalRightCoevaluationMorphismWithGivenSource
      1.8-8 TensorProductToInternalCoHomRightAdjunctMorphism
      1.8-9 TensorProductToInternalCoHomRightAdjunctMorphismWithGivenInternalCoHom
      1.8-10 InternalCoHomToTensorProductRightAdjunctMorphism
      1.8-11 InternalCoHomToTensorProductRightAdjunctMorphismWithGivenTensorProduct
      1.8-12 CoclosedMonoidalLeftEvaluationMorphism
      1.8-13 CoclosedMonoidalLeftEvaluationMorphismWithGivenRange
      1.8-14 CoclosedMonoidalLeftCoevaluationMorphism
      1.8-15 CoclosedMonoidalLeftCoevaluationMorphismWithGivenSource
      1.8-16 TensorProductToInternalCoHomLeftAdjunctMorphism
      1.8-17 TensorProductToInternalCoHomLeftAdjunctMorphismWithGivenInternalCoHom
      1.8-18 InternalCoHomToTensorProductLeftAdjunctMorphism
      1.8-19 InternalCoHomToTensorProductLeftAdjunctMorphismWithGivenTensorProduct
      1.8-20 MonoidalPreCoComposeMorphism
      1.8-21 MonoidalPreCoComposeMorphismWithGivenObjects
      1.8-22 MonoidalPostCoComposeMorphism
      1.8-23 MonoidalPostCoComposeMorphismWithGivenObjects
      1.8-24 CoDualOnObjects
      1.8-25 CoDualOnMorphisms
      1.8-26 CoDualOnMorphismsWithGivenCoDuals
      1.8-27 CoclosedEvaluationForCoDual
      1.8-28 CoclosedEvaluationForCoDualWithGivenTensorProduct
      1.8-29 MorphismFromCoBidual
      1.8-30 MorphismFromCoBidualWithGivenCoBidual
      1.8-31 InternalCoHomTensorProductCompatibilityMorphism
      1.8-32 InternalCoHomTensorProductCompatibilityMorphismWithGivenObjects
      1.8-33 CoDualityTensorProductCompatibilityMorphism
      1.8-34 CoDualityTensorProductCompatibilityMorphismWithGivenObjects
      1.8-35 MorphismFromInternalCoHomToTensorProduct
      1.8-36 MorphismFromInternalCoHomToTensorProductWithGivenObjects
      1.8-37 IsomorphismFromCoDualObjectToInternalCoHomFromTensorUnit
      1.8-38 IsomorphismFromInternalCoHomFromTensorUnitToCoDualObject
      1.8-39 UniversalPropertyOfCoDual
      1.8-40 CoLambdaIntroduction
      1.8-41 CoLambdaElimination
      1.8-42 IsomorphismFromObjectToInternalCoHom
      1.8-43 IsomorphismFromObjectToInternalCoHomWithGivenInternalCoHom
      1.8-44 IsomorphismFromInternalCoHomToObject
      1.8-45 IsomorphismFromInternalCoHomToObjectWithGivenInternalCoHom
    1.9 [33X[0;0YSymmetric Closed Monoidal Categories[133X
    1.10 [33X[0;0YSymmetric Coclosed Monoidal Categories[133X
    1.11 [33X[0;0YRigid Symmetric Closed Monoidal Categories[133X
      1.11-1 IsomorphismFromTensorProductWithDualObjectToInternalHom
      1.11-2 IsomorphismFromInternalHomToTensorProductWithDualObject
      1.11-3 MorphismFromInternalHomToTensorProduct
      1.11-4 MorphismFromInternalHomToTensorProductWithGivenObjects
      1.11-5 TensorProductInternalHomCompatibilityMorphismInverse
      1.11-6 TensorProductInternalHomCompatibilityMorphismInverseWithGivenObjects
      1.11-7 CoevaluationForDual
      1.11-8 CoevaluationForDualWithGivenTensorProduct
      1.11-9 TraceMap
      1.11-10 RankMorphism
      1.11-11 MorphismFromBidual
      1.11-12 MorphismFromBidualWithGivenBidual
    1.12 [33X[0;0YRigid Symmetric Coclosed Monoidal Categories[133X
      1.12-1 IsomorphismFromInternalCoHomToTensorProductWithCoDualObject
      1.12-2 IsomorphismFromTensorProductWithCoDualObjectToInternalCoHom
      1.12-3 MorphismFromTensorProductToInternalCoHom
      1.12-4 MorphismFromTensorProductToInternalCoHomWithGivenObjects
      1.12-5 InternalCoHomTensorProductCompatibilityMorphismInverse
      1.12-6 InternalCoHomTensorProductCompatibilityMorphismInverseWithGivenObjects
      1.12-7 CoclosedCoevaluationForCoDual
      1.12-8 CoclosedCoevaluationForCoDualWithGivenTensorProduct
      1.12-9 CoTraceMap
      1.12-10 CoRankMorphism
      1.12-11 MorphismToCoBidual
      1.12-12 MorphismToCoBidualWithGivenCoBidual
    1.13 [33X[0;0YConvenience Methods[133X
      1.13-1 InternalHom
      1.13-2 InternalCoHom
      1.13-3 LeftInternalHom
      1.13-4 LeftInternalCoHom
    1.14 [33X[0;0YAdd-methods[133X
      1.14-1 AddLeftDistributivityExpanding
      1.14-2 AddLeftDistributivityExpandingWithGivenObjects
      1.14-3 AddLeftDistributivityFactoring
      1.14-4 AddLeftDistributivityFactoringWithGivenObjects
      1.14-5 AddRightDistributivityExpanding
      1.14-6 AddRightDistributivityExpandingWithGivenObjects
      1.14-7 AddRightDistributivityFactoring
      1.14-8 AddRightDistributivityFactoringWithGivenObjects
      1.14-9 AddBraiding
      1.14-10 AddBraidingInverse
      1.14-11 AddBraidingInverseWithGivenTensorProducts
      1.14-12 AddBraidingWithGivenTensorProducts
      1.14-13 AddClosedMonoidalLeftCoevaluationMorphism
      1.14-14 AddClosedMonoidalLeftCoevaluationMorphismWithGivenRange
      1.14-15 AddClosedMonoidalLeftEvaluationMorphism
      1.14-16 AddClosedMonoidalLeftEvaluationMorphismWithGivenSource
      1.14-17 AddClosedMonoidalRightCoevaluationMorphism
      1.14-18 AddClosedMonoidalRightCoevaluationMorphismWithGivenRange
      1.14-19 AddClosedMonoidalRightEvaluationMorphism
      1.14-20 AddClosedMonoidalRightEvaluationMorphismWithGivenSource
      1.14-21 AddDualOnMorphisms
      1.14-22 AddDualOnMorphismsWithGivenDuals
      1.14-23 AddDualOnObjects
      1.14-24 AddEvaluationForDual
      1.14-25 AddEvaluationForDualWithGivenTensorProduct
      1.14-26 AddInternalHomOnMorphisms
      1.14-27 AddInternalHomOnMorphismsWithGivenInternalHoms
      1.14-28 AddInternalHomOnObjects
      1.14-29 AddInternalHomToTensorProductLeftAdjunctMorphism
      1.14-30 AddInternalHomToTensorProductLeftAdjunctMorphismWithGivenTensorProduct
      1.14-31 AddInternalHomToTensorProductLeftAdjunctionIsomorphism
      1.14-32 AddInternalHomToTensorProductLeftAdjunctionIsomorphismWithGivenObjects
      1.14-33 AddInternalHomToTensorProductRightAdjunctMorphism
      1.14-34 AddInternalHomToTensorProductRightAdjunctMorphismWithGivenTensorProduct
      1.14-35 AddInternalHomToTensorProductRightAdjunctionIsomorphism
      1.14-36 AddInternalHomToTensorProductRightAdjunctionIsomorphismWithGivenObjects
      1.14-37 AddIsomorphismFromDualObjectToInternalHomIntoTensorUnit
      1.14-38 AddIsomorphismFromInternalHomIntoTensorUnitToDualObject
      1.14-39 AddIsomorphismFromInternalHomToObject
      1.14-40 AddIsomorphismFromInternalHomToObjectWithGivenInternalHom
      1.14-41 AddIsomorphismFromObjectToInternalHom
      1.14-42 AddIsomorphismFromObjectToInternalHomWithGivenInternalHom
      1.14-43 AddLambdaElimination
      1.14-44 AddLambdaIntroduction
      1.14-45 AddMonoidalPostComposeMorphism
      1.14-46 AddMonoidalPostComposeMorphismWithGivenObjects
      1.14-47 AddMonoidalPreComposeMorphism
      1.14-48 AddMonoidalPreComposeMorphismWithGivenObjects
      1.14-49 AddMorphismFromTensorProductToInternalHom
      1.14-50 AddMorphismFromTensorProductToInternalHomWithGivenObjects
      1.14-51 AddMorphismToBidual
      1.14-52 AddMorphismToBidualWithGivenBidual
      1.14-53 AddTensorProductDualityCompatibilityMorphism
      1.14-54 AddTensorProductDualityCompatibilityMorphismWithGivenObjects
      1.14-55 AddTensorProductInternalHomCompatibilityMorphism
      1.14-56 AddTensorProductInternalHomCompatibilityMorphismWithGivenObjects
      1.14-57 AddTensorProductToInternalHomLeftAdjunctMorphism
      1.14-58 AddTensorProductToInternalHomLeftAdjunctMorphismWithGivenInternalHom
      1.14-59 AddTensorProductToInternalHomLeftAdjunctionIsomorphism
      1.14-60 AddTensorProductToInternalHomLeftAdjunctionIsomorphismWithGivenObjects
      1.14-61 AddTensorProductToInternalHomRightAdjunctMorphism
      1.14-62 AddTensorProductToInternalHomRightAdjunctMorphismWithGivenInternalHom
      1.14-63 AddTensorProductToInternalHomRightAdjunctionIsomorphism
      1.14-64 AddTensorProductToInternalHomRightAdjunctionIsomorphismWithGivenObjects
      1.14-65 AddUniversalPropertyOfDual
      1.14-66 AddCoDualOnMorphisms
      1.14-67 AddCoDualOnMorphismsWithGivenCoDuals
      1.14-68 AddCoDualOnObjects
      1.14-69 AddCoDualityTensorProductCompatibilityMorphism
      1.14-70 AddCoDualityTensorProductCompatibilityMorphismWithGivenObjects
      1.14-71 AddCoLambdaElimination
      1.14-72 AddCoLambdaIntroduction
      1.14-73 AddCoclosedEvaluationForCoDual
      1.14-74 AddCoclosedEvaluationForCoDualWithGivenTensorProduct
      1.14-75 AddCoclosedMonoidalLeftCoevaluationMorphism
      1.14-76 AddCoclosedMonoidalLeftCoevaluationMorphismWithGivenSource
      1.14-77 AddCoclosedMonoidalLeftEvaluationMorphism
      1.14-78 AddCoclosedMonoidalLeftEvaluationMorphismWithGivenRange
      1.14-79 AddCoclosedMonoidalRightCoevaluationMorphism
      1.14-80 AddCoclosedMonoidalRightCoevaluationMorphismWithGivenSource
      1.14-81 AddCoclosedMonoidalRightEvaluationMorphism
      1.14-82 AddCoclosedMonoidalRightEvaluationMorphismWithGivenRange
      1.14-83 AddInternalCoHomOnMorphisms
      1.14-84 AddInternalCoHomOnMorphismsWithGivenInternalCoHoms
      1.14-85 AddInternalCoHomOnObjects
      1.14-86 AddInternalCoHomTensorProductCompatibilityMorphism
      1.14-87 AddInternalCoHomTensorProductCompatibilityMorphismWithGivenObjects
      1.14-88 AddInternalCoHomToTensorProductLeftAdjunctMorphism
      1.14-89 AddInternalCoHomToTensorProductLeftAdjunctMorphismWithGivenTensorProduct
      1.14-90 AddInternalCoHomToTensorProductRightAdjunctMorphism
      1.14-91 AddInternalCoHomToTensorProductRightAdjunctMorphismWithGivenTensorProduct
      1.14-92 AddIsomorphismFromCoDualObjectToInternalCoHomFromTensorUnit
      1.14-93 AddIsomorphismFromInternalCoHomFromTensorUnitToCoDualObject
      1.14-94 AddIsomorphismFromInternalCoHomToObject
      1.14-95 AddIsomorphismFromInternalCoHomToObjectWithGivenInternalCoHom
      1.14-96 AddIsomorphismFromObjectToInternalCoHom
      1.14-97 AddIsomorphismFromObjectToInternalCoHomWithGivenInternalCoHom
      1.14-98 AddMonoidalPostCoComposeMorphism
      1.14-99 AddMonoidalPostCoComposeMorphismWithGivenObjects
      1.14-100 AddMonoidalPreCoComposeMorphism
      1.14-101 AddMonoidalPreCoComposeMorphismWithGivenObjects
      1.14-102 AddMorphismFromCoBidual
      1.14-103 AddMorphismFromCoBidualWithGivenCoBidual
      1.14-104 AddMorphismFromInternalCoHomToTensorProduct
      1.14-105 AddMorphismFromInternalCoHomToTensorProductWithGivenObjects
      1.14-106 AddTensorProductToInternalCoHomLeftAdjunctMorphism
      1.14-107 AddTensorProductToInternalCoHomLeftAdjunctMorphismWithGivenInternalCoHom
      1.14-108 AddTensorProductToInternalCoHomRightAdjunctMorphism
      1.14-109 AddTensorProductToInternalCoHomRightAdjunctMorphismWithGivenInternalCoHom
      1.14-110 AddUniversalPropertyOfCoDual
      1.14-111 AddIsomorphismFromLeftDualObjectToLeftInternalHomIntoTensorUnit
      1.14-112 AddIsomorphismFromLeftInternalHomIntoTensorUnitToLeftDualObject
      1.14-113 AddIsomorphismFromLeftInternalHomToObject
      1.14-114 AddIsomorphismFromLeftInternalHomToObjectWithGivenLeftInternalHom
      1.14-115 AddIsomorphismFromObjectToLeftInternalHom
      1.14-116 AddIsomorphismFromObjectToLeftInternalHomWithGivenLeftInternalHom
      1.14-117 AddLeftClosedMonoidalCoevaluationMorphism
      1.14-118 AddLeftClosedMonoidalCoevaluationMorphismWithGivenRange
      1.14-119 AddLeftClosedMonoidalEvaluationForLeftDual
      1.14-120 AddLeftClosedMonoidalEvaluationForLeftDualWithGivenTensorProduct
      1.14-121 AddLeftClosedMonoidalEvaluationMorphism
      1.14-122 AddLeftClosedMonoidalEvaluationMorphismWithGivenSource
      1.14-123 AddLeftClosedMonoidalLambdaElimination
      1.14-124 AddLeftClosedMonoidalLambdaIntroduction
      1.14-125 AddLeftClosedMonoidalPostComposeMorphism
      1.14-126 AddLeftClosedMonoidalPostComposeMorphismWithGivenObjects
      1.14-127 AddLeftClosedMonoidalPreComposeMorphism
      1.14-128 AddLeftClosedMonoidalPreComposeMorphismWithGivenObjects
      1.14-129 AddLeftDualOnMorphisms
      1.14-130 AddLeftDualOnMorphismsWithGivenLeftDuals
      1.14-131 AddLeftDualOnObjects
      1.14-132 AddLeftInternalHomOnMorphisms
      1.14-133 AddLeftInternalHomOnMorphismsWithGivenLeftInternalHoms
      1.14-134 AddLeftInternalHomOnObjects
      1.14-135 AddLeftInternalHomToTensorProductAdjunctMorphism
      1.14-136 AddLeftInternalHomToTensorProductAdjunctMorphismWithGivenTensorProduct
      1.14-137 AddMorphismFromTensorProductToLeftInternalHom
      1.14-138 AddMorphismFromTensorProductToLeftInternalHomWithGivenObjects
      1.14-139 AddMorphismToLeftBidual
      1.14-140 AddMorphismToLeftBidualWithGivenLeftBidual
      1.14-141 AddTensorProductLeftDualityCompatibilityMorphism
      1.14-142 AddTensorProductLeftDualityCompatibilityMorphismWithGivenObjects
      1.14-143 AddTensorProductLeftInternalHomCompatibilityMorphism
      1.14-144 AddTensorProductLeftInternalHomCompatibilityMorphismWithGivenObjects
      1.14-145 AddTensorProductToLeftInternalHomAdjunctMorphism
      1.14-146 AddTensorProductToLeftInternalHomAdjunctMorphismWithGivenLeftInternalHom
      1.14-147 AddUniversalPropertyOfLeftDual
      1.14-148 AddIsomorphismFromLeftCoDualObjectToLeftInternalCoHomFromTensorUnit
      1.14-149 AddIsomorphismFromLeftInternalCoHomFromTensorUnitToLeftCoDualObject
      1.14-150 AddIsomorphismFromLeftInternalCoHomToObject
      1.14-151 AddIsomorphismFromLeftInternalCoHomToObjectWithGivenLeftInternalCoHom
      1.14-152 AddIsomorphismFromObjectToLeftInternalCoHom
      1.14-153 AddIsomorphismFromObjectToLeftInternalCoHomWithGivenLeftInternalCoHom
      1.14-154 AddLeftCoDualOnMorphisms
      1.14-155 AddLeftCoDualOnMorphismsWithGivenLeftCoDuals
      1.14-156 AddLeftCoDualOnObjects
      1.14-157 AddLeftCoDualityTensorProductCompatibilityMorphism
      1.14-158 AddLeftCoDualityTensorProductCompatibilityMorphismWithGivenObjects
      1.14-159 AddLeftCoclosedMonoidalCoevaluationMorphism
      1.14-160 AddLeftCoclosedMonoidalCoevaluationMorphismWithGivenSource
      1.14-161 AddLeftCoclosedMonoidalEvaluationForLeftCoDual
      1.14-162 AddLeftCoclosedMonoidalEvaluationForLeftCoDualWithGivenTensorProduct
      1.14-163 AddLeftCoclosedMonoidalEvaluationMorphism
      1.14-164 AddLeftCoclosedMonoidalEvaluationMorphismWithGivenRange
      1.14-165 AddLeftCoclosedMonoidalLambdaElimination
      1.14-166 AddLeftCoclosedMonoidalLambdaIntroduction
      1.14-167 AddLeftCoclosedMonoidalPostCoComposeMorphism
      1.14-168 AddLeftCoclosedMonoidalPostCoComposeMorphismWithGivenObjects
      1.14-169 AddLeftCoclosedMonoidalPreCoComposeMorphism
      1.14-170 AddLeftCoclosedMonoidalPreCoComposeMorphismWithGivenObjects
      1.14-171 AddLeftInternalCoHomOnMorphisms
      1.14-172 AddLeftInternalCoHomOnMorphismsWithGivenLeftInternalCoHoms
      1.14-173 AddLeftInternalCoHomOnObjects
      1.14-174 AddLeftInternalCoHomTensorProductCompatibilityMorphism
      1.14-175 AddLeftInternalCoHomTensorProductCompatibilityMorphismWithGivenObjects
      1.14-176 AddLeftInternalCoHomToTensorProductAdjunctMorphism
      1.14-177 AddLeftInternalCoHomToTensorProductAdjunctMorphismWithGivenTensorProduct
      1.14-178 AddMorphismFromLeftCoBidual
      1.14-179 AddMorphismFromLeftCoBidualWithGivenLeftCoBidual
      1.14-180 AddMorphismFromLeftInternalCoHomToTensorProduct
      1.14-181 AddMorphismFromLeftInternalCoHomToTensorProductWithGivenObjects
      1.14-182 AddTensorProductToLeftInternalCoHomAdjunctMorphism
      1.14-183 AddTensorProductToLeftInternalCoHomAdjunctMorphismWithGivenLeftInternalCoHom
      1.14-184 AddUniversalPropertyOfLeftCoDual
      1.14-185 AddAssociatorLeftToRight
      1.14-186 AddAssociatorLeftToRightWithGivenTensorProducts
      1.14-187 AddAssociatorRightToLeft
      1.14-188 AddAssociatorRightToLeftWithGivenTensorProducts
      1.14-189 AddLeftUnitor
      1.14-190 AddLeftUnitorInverse
      1.14-191 AddLeftUnitorInverseWithGivenTensorProduct
      1.14-192 AddLeftUnitorWithGivenTensorProduct
      1.14-193 AddRightUnitor
      1.14-194 AddRightUnitorInverse
      1.14-195 AddRightUnitorInverseWithGivenTensorProduct
      1.14-196 AddRightUnitorWithGivenTensorProduct
      1.14-197 AddTensorProductOnMorphisms
      1.14-198 AddTensorProductOnMorphismsWithGivenTensorProducts
      1.14-199 AddCoevaluationForDual
      1.14-200 AddCoevaluationForDualWithGivenTensorProduct
      1.14-201 AddIsomorphismFromInternalHomToTensorProductWithDualObject
      1.14-202 AddIsomorphismFromTensorProductWithDualObjectToInternalHom
      1.14-203 AddMorphismFromBidual
      1.14-204 AddMorphismFromBidualWithGivenBidual
      1.14-205 AddMorphismFromInternalHomToTensorProduct
      1.14-206 AddMorphismFromInternalHomToTensorProductWithGivenObjects
      1.14-207 AddRankMorphism
      1.14-208 AddTensorProductInternalHomCompatibilityMorphismInverse
      1.14-209 AddTensorProductInternalHomCompatibilityMorphismInverseWithGivenObjects
      1.14-210 AddTraceMap
      1.14-211 AddCoRankMorphism
      1.14-212 AddCoTraceMap
      1.14-213 AddCoclosedCoevaluationForCoDual
      1.14-214 AddCoclosedCoevaluationForCoDualWithGivenTensorProduct
      1.14-215 AddInternalCoHomTensorProductCompatibilityMorphismInverse
      1.14-216 AddInternalCoHomTensorProductCompatibilityMorphismInverseWithGivenObjects
      1.14-217 AddIsomorphismFromInternalCoHomToTensorProductWithCoDualObject
      1.14-218 AddIsomorphismFromTensorProductWithCoDualObjectToInternalCoHom
      1.14-219 AddMorphismFromTensorProductToInternalCoHom
      1.14-220 AddMorphismFromTensorProductToInternalCoHomWithGivenObjects
      1.14-221 AddMorphismToCoBidual
      1.14-222 AddMorphismToCoBidualWithGivenCoBidual
  2 [33X[0;0YExamples and Tests[133X
    2.1 [33X[0;0YTest functions[133X
      2.1-1 AdditiveMonoidalCategoriesTest
      2.1-2 BraidedMonoidalCategoriesTest
      2.1-3 ClosedMonoidalCategoriesTest
      2.1-4 ClosedMonoidalCategoriesTestWithGiven
      2.1-5 CoclosedMonoidalCategoriesTest
      2.1-6 CoclosedMonoidalCategoriesTestWithGiven
      2.1-7 LeftClosedMonoidalCategoriesTest
      2.1-8 LeftClosedMonoidalCategoriesTestWithGiven
      2.1-9 LeftCoclosedMonoidalCategoriesTest
      2.1-10 LeftCoclosedMonoidalCategoriesTestWithGiven
      2.1-11 MonoidalCategoriesTensorProductAndUnitTest
      2.1-12 MonoidalCategoriesTest
      2.1-13 RigidSymmetricClosedMonoidalCategoriesTest
      2.1-14 RigidSymmetricCoclosedMonoidalCategoriesTest
    2.2 [33X[0;0YBasics[133X
  3 [33X[0;0YCode Generation for Monodial Categories[133X
    3.1 [33X[0;0YMonoidal Categories[133X
      3.1-1 WriteFileForMonoidalStructure
    3.2 [33X[0;0YClosed Monoidal Categories[133X
      3.2-1 WriteFileForClosedMonoidalStructure
      3.2-2 WriteFileForLeftClosedMonoidalStructure
    3.3 [33X[0;0YCoclosed Monoidal Categories[133X
      3.3-1 WriteFileForCoclosedMonoidalStructure
      3.3-2 WriteFileForLeftCoclosedMonoidalStructure
  4 [33X[0;0YThe terminal category with multiple objects[133X
    4.1 [33X[0;0YConstructors[133X
    4.2 [33X[0;0Y[5XGAP[105X Categories[133X
  5 [33X[0;0YLegacy Operations and Synonyms[133X
    5.1 [33X[0;0YLegacy operations[133X
      5.1-1 CoclosedCoevaluationMorphism
      5.1-2 CoclosedCoevaluationMorphismWithGivenSource
      5.1-3 CoclosedEvaluationMorphism
      5.1-4 CoclosedEvaluationMorphismWithGivenRange
      5.1-5 CoevaluationMorphism
      5.1-6 CoevaluationMorphismWithGivenRange
    5.2 [33X[0;0YSynonyms for legacy operations[133X
      5.2-1 EvaluationMorphism
      5.2-2 EvaluationMorphismWithGivenSource
      5.2-3 InternalCoHomToTensorProductAdjunctionMap
      5.2-4 InternalCoHomToTensorProductAdjunctionMapWithGivenTensorProduct
      5.2-5 InternalHomToTensorProductAdjunctionMap
      5.2-6 InternalHomToTensorProductAdjunctionMapWithGivenTensorProduct
      5.2-7 TensorProductToInternalCoHomAdjunctionMap
      5.2-8 TensorProductToInternalCoHomAdjunctionMapWithGivenInternalCoHom
      5.2-9 TensorProductToInternalHomAdjunctionMap
      5.2-10 TensorProductToInternalHomAdjunctionMapWithGivenInternalHom
      5.2-11 InternalCoHomToTensorProductLeftAdjunctionMap
      5.2-12 InternalHomToTensorProductLeftAdjunctionMap
      5.2-13 TensorProductToInternalCoHomLeftAdjunctionMap
      5.2-14 TensorProductToInternalCoHomLeftAdjunctionMapWithGivenInternalCoHom
      5.2-15 TensorProductToInternalHomLeftAdjunctionMap
      5.2-16 TensorProductToInternalHomLeftAdjunctionMapWithGivenInternalHom
  6 [33X[0;0YMonoidalCategories automatic generated documentation[133X
    6.1 [33X[0;0YMonoidalCategories automatic generated documentation of properties[133X
      6.1-1 IsBraidedMonoidalCategory
      6.1-2 IsClosedMonoidalCategory
      6.1-3 IsCoclosedMonoidalCategory
      6.1-4 IsLeftClosedMonoidalCategory
      6.1-5 IsLeftCoclosedMonoidalCategory
      6.1-6 IsMonoidalCategory
      6.1-7 IsStrictMonoidalCategory
      6.1-8 IsRigidSymmetricClosedMonoidalCategory
      6.1-9 IsRigidSymmetricCoclosedMonoidalCategory
      6.1-10 IsSymmetricClosedMonoidalCategory
      6.1-11 IsSymmetricCoclosedMonoidalCategory
      6.1-12 IsSymmetricMonoidalCategory
  
  
  [32X
