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MonoidalCategories

Monoidal and monoidal (co)closed categories

2020.10-01

19 October 2020

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

Contents

1 Monoidal Categories
 1.5 Closed Monoidal Categories

  1.5-1 InternalHomOnObjects

  1.5-2 AddInternalHomOnObjects

  1.5-3 InternalHomOnMorphisms

  1.5-4 InternalHomOnMorphismsWithGivenInternalHoms

  1.5-5 AddInternalHomOnMorphismsWithGivenInternalHoms

  1.5-6 EvaluationMorphism

  1.5-7 EvaluationMorphismWithGivenSource

  1.5-8 AddEvaluationMorphismWithGivenSource

  1.5-9 CoevaluationMorphism

  1.5-10 CoevaluationMorphismWithGivenRange

  1.5-11 AddCoevaluationMorphismWithGivenRange

  1.5-12 TensorProductToInternalHomAdjunctionMap

  1.5-13 AddTensorProductToInternalHomAdjunctionMap

  1.5-14 InternalHomToTensorProductAdjunctionMap

  1.5-15 AddInternalHomToTensorProductAdjunctionMap

  1.5-16 MonoidalPreComposeMorphism

  1.5-17 MonoidalPreComposeMorphismWithGivenObjects

  1.5-18 AddMonoidalPreComposeMorphismWithGivenObjects

  1.5-19 MonoidalPostComposeMorphism

  1.5-20 MonoidalPostComposeMorphismWithGivenObjects

  1.5-21 AddMonoidalPostComposeMorphismWithGivenObjects

  1.5-22 DualOnObjects

  1.5-23 AddDualOnObjects

  1.5-24 DualOnMorphisms

  1.5-25 DualOnMorphismsWithGivenDuals

  1.5-26 AddDualOnMorphismsWithGivenDuals

  1.5-27 EvaluationForDual

  1.5-28 EvaluationForDualWithGivenTensorProduct

  1.5-29 AddEvaluationForDualWithGivenTensorProduct

  1.5-30 MorphismToBidual

  1.5-31 MorphismToBidualWithGivenBidual

  1.5-32 AddMorphismToBidualWithGivenBidual

  1.5-33 TensorProductInternalHomCompatibilityMorphism

  1.5-34 TensorProductInternalHomCompatibilityMorphismWithGivenObjects

  1.5-35 AddTensorProductInternalHomCompatibilityMorphismWithGivenObjects

  1.5-36 TensorProductDualityCompatibilityMorphism

  1.5-37 TensorProductDualityCompatibilityMorphismWithGivenObjects

  1.5-38 AddTensorProductDualityCompatibilityMorphismWithGivenObjects

  1.5-39 MorphismFromTensorProductToInternalHom

  1.5-40 MorphismFromTensorProductToInternalHomWithGivenObjects

  1.5-41 AddMorphismFromTensorProductToInternalHomWithGivenObjects

  1.5-42 IsomorphismFromDualToInternalHom

  1.5-43 AddIsomorphismFromDualToInternalHom

  1.5-44 IsomorphismFromInternalHomToDual

  1.5-45 AddIsomorphismFromInternalHomToDual

  1.5-46 UniversalPropertyOfDual

  1.5-47 AddUniversalPropertyOfDual

  1.5-48 LambdaIntroduction

  1.5-49 AddLambdaIntroduction

  1.5-50 LambdaElimination

  1.5-51 AddLambdaElimination

  1.5-52 IsomorphismFromObjectToInternalHom

  1.5-53 IsomorphismFromObjectToInternalHomWithGivenInternalHom

  1.5-54 AddIsomorphismFromObjectToInternalHomWithGivenInternalHom

  1.5-55 IsomorphismFromInternalHomToObject

  1.5-56 IsomorphismFromInternalHomToObjectWithGivenInternalHom

  1.5-57 AddIsomorphismFromInternalHomToObjectWithGivenInternalHom
Index

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