Goto Chapter: Top 1 2 3 4 5 6 Ind
 [Top of Book]  [Contents]   [Next Chapter] 

MonoidalCategories

Monoidal and monoidal (co)closed categories

2024.09-05

12 September 2024

Mohamed Barakat
Email: mohamed.barakat@uni-siegen.de
Homepage: http://algebra.mathematik.uni-siegen.de/barakat/
Address:
Walter-Flex-Str. 3
57068 Siegen
Germany

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

Sebastian Posur
Email: sebastian.posur@uni-siegen.de
Homepage: http://algebra.mathematik.uni-siegen.de/posur/
Address:
Department Mathematik
Universität Siegen
Walter-Flex-Straße 3
57068 Siegen
Germany

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

Fabian Zickgraf
Email: fabian.zickgraf@uni-siegen.de
Homepage: https://github.com/zickgraf/
Address:
Walter-Flex-Str. 3
57068 Siegen
Germany

Contents

1 Monoidal Categories
 1.5 Left Closed Monoidal Categories

  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 Closed Monoidal Categories

  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 Left Coclosed Monoidal Categories

  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 Coclosed Monoidal Categories

  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
 1.14 Add-methods

  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 AddTensorProductOnObjects

  1.14-200 AddTensorUnit

  1.14-201 AddCoevaluationForDual

  1.14-202 AddCoevaluationForDualWithGivenTensorProduct

  1.14-203 AddIsomorphismFromInternalHomToTensorProductWithDualObject

  1.14-204 AddIsomorphismFromTensorProductWithDualObjectToInternalHom

  1.14-205 AddMorphismFromBidual

  1.14-206 AddMorphismFromBidualWithGivenBidual

  1.14-207 AddMorphismFromInternalHomToTensorProduct

  1.14-208 AddMorphismFromInternalHomToTensorProductWithGivenObjects

  1.14-209 AddRankMorphism

  1.14-210 AddTensorProductInternalHomCompatibilityMorphismInverse

  1.14-211 AddTensorProductInternalHomCompatibilityMorphismInverseWithGivenObjects

  1.14-212 AddTraceMap

  1.14-213 AddCoRankMorphism

  1.14-214 AddCoTraceMap

  1.14-215 AddCoclosedCoevaluationForCoDual

  1.14-216 AddCoclosedCoevaluationForCoDualWithGivenTensorProduct

  1.14-217 AddInternalCoHomTensorProductCompatibilityMorphismInverse

  1.14-218 AddInternalCoHomTensorProductCompatibilityMorphismInverseWithGivenObjects

  1.14-219 AddIsomorphismFromInternalCoHomToTensorProductWithCoDualObject

  1.14-220 AddIsomorphismFromTensorProductWithCoDualObjectToInternalCoHom

  1.14-221 AddMorphismFromTensorProductToInternalCoHom

  1.14-222 AddMorphismFromTensorProductToInternalCoHomWithGivenObjects

  1.14-223 AddMorphismToCoBidual

  1.14-224 AddMorphismToCoBidualWithGivenCoBidual
2 Examples and Tests
3 Code Generation for Monodial Categories
4 The terminal category with multiple objects
5 Legacy Operations and Synonyms
6 MonoidalCategories automatic generated documentation
Index

 [Top of Book]  [Contents]   [Next Chapter] 
Goto Chapter: Top 1 2 3 4 5 6 Ind

generated by GAPDoc2HTML