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MonoidalCategories

Monoidal and monoidal (co)closed categories

2024.02-04

28 February 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 InternalHomToTensorProductRightAdjunctMorphism

  1.6-11 InternalHomToTensorProductRightAdjunctMorphismWithGivenTensorProduct

  1.6-12 ClosedMonoidalLeftEvaluationMorphism

  1.6-13 ClosedMonoidalLeftEvaluationMorphismWithGivenSource

  1.6-14 ClosedMonoidalLeftCoevaluationMorphism

  1.6-15 ClosedMonoidalLeftCoevaluationMorphismWithGivenRange

  1.6-16 TensorProductToInternalHomLeftAdjunctMorphism

  1.6-17 TensorProductToInternalHomLeftAdjunctMorphismWithGivenInternalHom

  1.6-18 InternalHomToTensorProductLeftAdjunctMorphism

  1.6-19 InternalHomToTensorProductLeftAdjunctMorphismWithGivenTensorProduct

  1.6-20 MonoidalPreComposeMorphism

  1.6-21 MonoidalPreComposeMorphismWithGivenObjects

  1.6-22 MonoidalPostComposeMorphism

  1.6-23 MonoidalPostComposeMorphismWithGivenObjects

  1.6-24 DualOnObjects

  1.6-25 DualOnMorphisms

  1.6-26 DualOnMorphismsWithGivenDuals

  1.6-27 EvaluationForDual

  1.6-28 EvaluationForDualWithGivenTensorProduct

  1.6-29 MorphismToBidual

  1.6-30 MorphismToBidualWithGivenBidual

  1.6-31 TensorProductInternalHomCompatibilityMorphism

  1.6-32 TensorProductInternalHomCompatibilityMorphismWithGivenObjects

  1.6-33 TensorProductDualityCompatibilityMorphism

  1.6-34 TensorProductDualityCompatibilityMorphismWithGivenObjects

  1.6-35 MorphismFromTensorProductToInternalHom

  1.6-36 MorphismFromTensorProductToInternalHomWithGivenObjects

  1.6-37 IsomorphismFromDualObjectToInternalHomIntoTensorUnit

  1.6-38 IsomorphismFromInternalHomIntoTensorUnitToDualObject

  1.6-39 UniversalPropertyOfDual

  1.6-40 LambdaIntroduction

  1.6-41 LambdaElimination

  1.6-42 IsomorphismFromObjectToInternalHom

  1.6-43 IsomorphismFromObjectToInternalHomWithGivenInternalHom

  1.6-44 IsomorphismFromInternalHomToObject

  1.6-45 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 AddInternalHomToTensorProductRightAdjunctMorphism

  1.14-32 AddInternalHomToTensorProductRightAdjunctMorphismWithGivenTensorProduct

  1.14-33 AddIsomorphismFromDualObjectToInternalHomIntoTensorUnit

  1.14-34 AddIsomorphismFromInternalHomIntoTensorUnitToDualObject

  1.14-35 AddIsomorphismFromInternalHomToObject

  1.14-36 AddIsomorphismFromInternalHomToObjectWithGivenInternalHom

  1.14-37 AddIsomorphismFromObjectToInternalHom

  1.14-38 AddIsomorphismFromObjectToInternalHomWithGivenInternalHom

  1.14-39 AddLambdaElimination

  1.14-40 AddLambdaIntroduction

  1.14-41 AddMonoidalPostComposeMorphism

  1.14-42 AddMonoidalPostComposeMorphismWithGivenObjects

  1.14-43 AddMonoidalPreComposeMorphism

  1.14-44 AddMonoidalPreComposeMorphismWithGivenObjects

  1.14-45 AddMorphismFromTensorProductToInternalHom

  1.14-46 AddMorphismFromTensorProductToInternalHomWithGivenObjects

  1.14-47 AddMorphismToBidual

  1.14-48 AddMorphismToBidualWithGivenBidual

  1.14-49 AddTensorProductDualityCompatibilityMorphism

  1.14-50 AddTensorProductDualityCompatibilityMorphismWithGivenObjects

  1.14-51 AddTensorProductInternalHomCompatibilityMorphism

  1.14-52 AddTensorProductInternalHomCompatibilityMorphismWithGivenObjects

  1.14-53 AddTensorProductToInternalHomLeftAdjunctMorphism

  1.14-54 AddTensorProductToInternalHomLeftAdjunctMorphismWithGivenInternalHom

  1.14-55 AddTensorProductToInternalHomRightAdjunctMorphism

  1.14-56 AddTensorProductToInternalHomRightAdjunctMorphismWithGivenInternalHom

  1.14-57 AddUniversalPropertyOfDual

  1.14-58 AddCoDualOnMorphisms

  1.14-59 AddCoDualOnMorphismsWithGivenCoDuals

  1.14-60 AddCoDualOnObjects

  1.14-61 AddCoDualityTensorProductCompatibilityMorphism

  1.14-62 AddCoDualityTensorProductCompatibilityMorphismWithGivenObjects

  1.14-63 AddCoLambdaElimination

  1.14-64 AddCoLambdaIntroduction

  1.14-65 AddCoclosedEvaluationForCoDual

  1.14-66 AddCoclosedEvaluationForCoDualWithGivenTensorProduct

  1.14-67 AddCoclosedMonoidalLeftCoevaluationMorphism

  1.14-68 AddCoclosedMonoidalLeftCoevaluationMorphismWithGivenSource

  1.14-69 AddCoclosedMonoidalLeftEvaluationMorphism

  1.14-70 AddCoclosedMonoidalLeftEvaluationMorphismWithGivenRange

  1.14-71 AddCoclosedMonoidalRightCoevaluationMorphism

  1.14-72 AddCoclosedMonoidalRightCoevaluationMorphismWithGivenSource

  1.14-73 AddCoclosedMonoidalRightEvaluationMorphism

  1.14-74 AddCoclosedMonoidalRightEvaluationMorphismWithGivenRange

  1.14-75 AddInternalCoHomOnMorphisms

  1.14-76 AddInternalCoHomOnMorphismsWithGivenInternalCoHoms

  1.14-77 AddInternalCoHomOnObjects

  1.14-78 AddInternalCoHomTensorProductCompatibilityMorphism

  1.14-79 AddInternalCoHomTensorProductCompatibilityMorphismWithGivenObjects

  1.14-80 AddInternalCoHomToTensorProductLeftAdjunctMorphism

  1.14-81 AddInternalCoHomToTensorProductLeftAdjunctMorphismWithGivenTensorProduct

  1.14-82 AddInternalCoHomToTensorProductRightAdjunctMorphism

  1.14-83 AddInternalCoHomToTensorProductRightAdjunctMorphismWithGivenTensorProduct

  1.14-84 AddIsomorphismFromCoDualObjectToInternalCoHomFromTensorUnit

  1.14-85 AddIsomorphismFromInternalCoHomFromTensorUnitToCoDualObject

  1.14-86 AddIsomorphismFromInternalCoHomToObject

  1.14-87 AddIsomorphismFromInternalCoHomToObjectWithGivenInternalCoHom

  1.14-88 AddIsomorphismFromObjectToInternalCoHom

  1.14-89 AddIsomorphismFromObjectToInternalCoHomWithGivenInternalCoHom

  1.14-90 AddMonoidalPostCoComposeMorphism

  1.14-91 AddMonoidalPostCoComposeMorphismWithGivenObjects

  1.14-92 AddMonoidalPreCoComposeMorphism

  1.14-93 AddMonoidalPreCoComposeMorphismWithGivenObjects

  1.14-94 AddMorphismFromCoBidual

  1.14-95 AddMorphismFromCoBidualWithGivenCoBidual

  1.14-96 AddMorphismFromInternalCoHomToTensorProduct

  1.14-97 AddMorphismFromInternalCoHomToTensorProductWithGivenObjects

  1.14-98 AddTensorProductToInternalCoHomLeftAdjunctMorphism

  1.14-99 AddTensorProductToInternalCoHomLeftAdjunctMorphismWithGivenInternalCoHom

  1.14-100 AddTensorProductToInternalCoHomRightAdjunctMorphism

  1.14-101 AddTensorProductToInternalCoHomRightAdjunctMorphismWithGivenInternalCoHom

  1.14-102 AddUniversalPropertyOfCoDual

  1.14-103 AddIsomorphismFromLeftDualObjectToLeftInternalHomIntoTensorUnit

  1.14-104 AddIsomorphismFromLeftInternalHomIntoTensorUnitToLeftDualObject

  1.14-105 AddIsomorphismFromLeftInternalHomToObject

  1.14-106 AddIsomorphismFromLeftInternalHomToObjectWithGivenLeftInternalHom

  1.14-107 AddIsomorphismFromObjectToLeftInternalHom

  1.14-108 AddIsomorphismFromObjectToLeftInternalHomWithGivenLeftInternalHom

  1.14-109 AddLeftClosedMonoidalCoevaluationMorphism

  1.14-110 AddLeftClosedMonoidalCoevaluationMorphismWithGivenRange

  1.14-111 AddLeftClosedMonoidalEvaluationForLeftDual

  1.14-112 AddLeftClosedMonoidalEvaluationForLeftDualWithGivenTensorProduct

  1.14-113 AddLeftClosedMonoidalEvaluationMorphism

  1.14-114 AddLeftClosedMonoidalEvaluationMorphismWithGivenSource

  1.14-115 AddLeftClosedMonoidalLambdaElimination

  1.14-116 AddLeftClosedMonoidalLambdaIntroduction

  1.14-117 AddLeftClosedMonoidalPostComposeMorphism

  1.14-118 AddLeftClosedMonoidalPostComposeMorphismWithGivenObjects

  1.14-119 AddLeftClosedMonoidalPreComposeMorphism

  1.14-120 AddLeftClosedMonoidalPreComposeMorphismWithGivenObjects

  1.14-121 AddLeftDualOnMorphisms

  1.14-122 AddLeftDualOnMorphismsWithGivenLeftDuals

  1.14-123 AddLeftDualOnObjects

  1.14-124 AddLeftInternalHomOnMorphisms

  1.14-125 AddLeftInternalHomOnMorphismsWithGivenLeftInternalHoms

  1.14-126 AddLeftInternalHomOnObjects

  1.14-127 AddLeftInternalHomToTensorProductAdjunctMorphism

  1.14-128 AddLeftInternalHomToTensorProductAdjunctMorphismWithGivenTensorProduct

  1.14-129 AddMorphismFromTensorProductToLeftInternalHom

  1.14-130 AddMorphismFromTensorProductToLeftInternalHomWithGivenObjects

  1.14-131 AddMorphismToLeftBidual

  1.14-132 AddMorphismToLeftBidualWithGivenLeftBidual

  1.14-133 AddTensorProductLeftDualityCompatibilityMorphism

  1.14-134 AddTensorProductLeftDualityCompatibilityMorphismWithGivenObjects

  1.14-135 AddTensorProductLeftInternalHomCompatibilityMorphism

  1.14-136 AddTensorProductLeftInternalHomCompatibilityMorphismWithGivenObjects

  1.14-137 AddTensorProductToLeftInternalHomAdjunctMorphism

  1.14-138 AddTensorProductToLeftInternalHomAdjunctMorphismWithGivenLeftInternalHom

  1.14-139 AddUniversalPropertyOfLeftDual

  1.14-140 AddIsomorphismFromLeftCoDualObjectToLeftInternalCoHomFromTensorUnit

  1.14-141 AddIsomorphismFromLeftInternalCoHomFromTensorUnitToLeftCoDualObject

  1.14-142 AddIsomorphismFromLeftInternalCoHomToObject

  1.14-143 AddIsomorphismFromLeftInternalCoHomToObjectWithGivenLeftInternalCoHom

  1.14-144 AddIsomorphismFromObjectToLeftInternalCoHom

  1.14-145 AddIsomorphismFromObjectToLeftInternalCoHomWithGivenLeftInternalCoHom

  1.14-146 AddLeftCoDualOnMorphisms

  1.14-147 AddLeftCoDualOnMorphismsWithGivenLeftCoDuals

  1.14-148 AddLeftCoDualOnObjects

  1.14-149 AddLeftCoDualityTensorProductCompatibilityMorphism

  1.14-150 AddLeftCoDualityTensorProductCompatibilityMorphismWithGivenObjects

  1.14-151 AddLeftCoclosedMonoidalCoevaluationMorphism

  1.14-152 AddLeftCoclosedMonoidalCoevaluationMorphismWithGivenSource

  1.14-153 AddLeftCoclosedMonoidalEvaluationForLeftCoDual

  1.14-154 AddLeftCoclosedMonoidalEvaluationForLeftCoDualWithGivenTensorProduct

  1.14-155 AddLeftCoclosedMonoidalEvaluationMorphism

  1.14-156 AddLeftCoclosedMonoidalEvaluationMorphismWithGivenRange

  1.14-157 AddLeftCoclosedMonoidalLambdaElimination

  1.14-158 AddLeftCoclosedMonoidalLambdaIntroduction

  1.14-159 AddLeftCoclosedMonoidalPostCoComposeMorphism

  1.14-160 AddLeftCoclosedMonoidalPostCoComposeMorphismWithGivenObjects

  1.14-161 AddLeftCoclosedMonoidalPreCoComposeMorphism

  1.14-162 AddLeftCoclosedMonoidalPreCoComposeMorphismWithGivenObjects

  1.14-163 AddLeftInternalCoHomOnMorphisms

  1.14-164 AddLeftInternalCoHomOnMorphismsWithGivenLeftInternalCoHoms

  1.14-165 AddLeftInternalCoHomOnObjects

  1.14-166 AddLeftInternalCoHomTensorProductCompatibilityMorphism

  1.14-167 AddLeftInternalCoHomTensorProductCompatibilityMorphismWithGivenObjects

  1.14-168 AddLeftInternalCoHomToTensorProductAdjunctMorphism

  1.14-169 AddLeftInternalCoHomToTensorProductAdjunctMorphismWithGivenTensorProduct

  1.14-170 AddMorphismFromLeftCoBidual

  1.14-171 AddMorphismFromLeftCoBidualWithGivenLeftCoBidual

  1.14-172 AddMorphismFromLeftInternalCoHomToTensorProduct

  1.14-173 AddMorphismFromLeftInternalCoHomToTensorProductWithGivenObjects

  1.14-174 AddTensorProductToLeftInternalCoHomAdjunctMorphism

  1.14-175 AddTensorProductToLeftInternalCoHomAdjunctMorphismWithGivenLeftInternalCoHom

  1.14-176 AddUniversalPropertyOfLeftCoDual

  1.14-177 AddAssociatorLeftToRight

  1.14-178 AddAssociatorLeftToRightWithGivenTensorProducts

  1.14-179 AddAssociatorRightToLeft

  1.14-180 AddAssociatorRightToLeftWithGivenTensorProducts

  1.14-181 AddLeftUnitor

  1.14-182 AddLeftUnitorInverse

  1.14-183 AddLeftUnitorInverseWithGivenTensorProduct

  1.14-184 AddLeftUnitorWithGivenTensorProduct

  1.14-185 AddRightUnitor

  1.14-186 AddRightUnitorInverse

  1.14-187 AddRightUnitorInverseWithGivenTensorProduct

  1.14-188 AddRightUnitorWithGivenTensorProduct

  1.14-189 AddTensorProductOnMorphisms

  1.14-190 AddTensorProductOnMorphismsWithGivenTensorProducts

  1.14-191 AddCoevaluationForDual

  1.14-192 AddCoevaluationForDualWithGivenTensorProduct

  1.14-193 AddIsomorphismFromInternalHomToTensorProductWithDualObject

  1.14-194 AddIsomorphismFromTensorProductWithDualObjectToInternalHom

  1.14-195 AddMorphismFromBidual

  1.14-196 AddMorphismFromBidualWithGivenBidual

  1.14-197 AddMorphismFromInternalHomToTensorProduct

  1.14-198 AddMorphismFromInternalHomToTensorProductWithGivenObjects

  1.14-199 AddRankMorphism

  1.14-200 AddTensorProductInternalHomCompatibilityMorphismInverse

  1.14-201 AddTensorProductInternalHomCompatibilityMorphismInverseWithGivenObjects

  1.14-202 AddTraceMap

  1.14-203 AddCoRankMorphism

  1.14-204 AddCoTraceMap

  1.14-205 AddCoclosedCoevaluationForCoDual

  1.14-206 AddCoclosedCoevaluationForCoDualWithGivenTensorProduct

  1.14-207 AddInternalCoHomTensorProductCompatibilityMorphismInverse

  1.14-208 AddInternalCoHomTensorProductCompatibilityMorphismInverseWithGivenObjects

  1.14-209 AddIsomorphismFromInternalCoHomToTensorProductWithCoDualObject

  1.14-210 AddIsomorphismFromTensorProductWithCoDualObjectToInternalCoHom

  1.14-211 AddMorphismFromTensorProductToInternalCoHom

  1.14-212 AddMorphismFromTensorProductToInternalCoHomWithGivenObjects

  1.14-213 AddMorphismToCoBidual

  1.14-214 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

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