  
  
                              [1X MonoidalCategories [101X
  
  
                 [1X Monoidal and monoidal (co)closed categories [101X
  
  
                                   2020.10-01
  
  
                                19 October 2020
  
  
                                Mohamed Barakat
  
                               Sebastian Gutsche
  
                                Sebastian Posur
  
  
  
  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
  
  
  
  -------------------------------------------------------
  
  
  [1XContents (MonoidalCategories)[101X
  
  1 [33X[0;0YMonoidal Categories[133X
    1.1 [33X[0;0YMonoidal Categories[133X
      1.1-1 TensorProductOnObjects
      1.1-2 AddTensorProductOnObjects
      1.1-3 TensorUnit
      1.1-4 AddTensorUnit
      1.1-5 TensorProductOnMorphisms
      1.1-6 TensorProductOnMorphismsWithGivenTensorProducts
      1.1-7 AddTensorProductOnMorphismsWithGivenTensorProducts
      1.1-8 AssociatorRightToLeft
      1.1-9 AssociatorRightToLeftWithGivenTensorProducts
      1.1-10 AddAssociatorRightToLeftWithGivenTensorProducts
      1.1-11 AssociatorLeftToRight
      1.1-12 AssociatorLeftToRightWithGivenTensorProducts
      1.1-13 AddAssociatorLeftToRightWithGivenTensorProducts
      1.1-14 LeftUnitor
      1.1-15 LeftUnitorWithGivenTensorProduct
      1.1-16 AddLeftUnitorWithGivenTensorProduct
      1.1-17 LeftUnitorInverse
      1.1-18 LeftUnitorInverseWithGivenTensorProduct
      1.1-19 AddLeftUnitorInverseWithGivenTensorProduct
      1.1-20 RightUnitor
      1.1-21 RightUnitorWithGivenTensorProduct
      1.1-22 AddRightUnitorWithGivenTensorProduct
      1.1-23 RightUnitorInverse
      1.1-24 RightUnitorInverseWithGivenTensorProduct
      1.1-25 AddRightUnitorInverseWithGivenTensorProduct
    1.2 [33X[0;0YAdditive Monoidal Categories[133X
      1.2-1 LeftDistributivityExpanding
      1.2-2 LeftDistributivityExpandingWithGivenObjects
      1.2-3 AddLeftDistributivityExpandingWithGivenObjects
      1.2-4 LeftDistributivityFactoring
      1.2-5 LeftDistributivityFactoringWithGivenObjects
      1.2-6 AddLeftDistributivityFactoringWithGivenObjects
      1.2-7 RightDistributivityExpanding
      1.2-8 RightDistributivityExpandingWithGivenObjects
      1.2-9 AddRightDistributivityExpandingWithGivenObjects
      1.2-10 RightDistributivityFactoring
      1.2-11 RightDistributivityFactoringWithGivenObjects
      1.2-12 AddRightDistributivityFactoringWithGivenObjects
    1.3 [33X[0;0YBraided Monoidal Categories[133X
      1.3-1 Braiding
      1.3-2 BraidingWithGivenTensorProducts
      1.3-3 AddBraidingWithGivenTensorProducts
      1.3-4 BraidingInverse
      1.3-5 BraidingInverseWithGivenTensorProducts
      1.3-6 AddBraidingInverseWithGivenTensorProducts
    1.4 [33X[0;0YSymmetric Monoidal Categories[133X
    1.5 [33X[0;0YClosed Monoidal Categories[133X
      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
    1.6 [33X[0;0YSymmetric Closed Monoidal Categories[133X
    1.7 [33X[0;0YRigid Symmetric Closed Monoidal Categories[133X
      1.7-1 IsomorphismFromTensorProductToInternalHom
      1.7-2 AddIsomorphismFromTensorProductToInternalHom
      1.7-3 MorphismFromInternalHomToTensorProduct
      1.7-4 MorphismFromInternalHomToTensorProductWithGivenObjects
      1.7-5 AddMorphismFromInternalHomToTensorProductWithGivenObjects
      1.7-6 IsomorphismFromInternalHomToTensorProduct
      1.7-7 AddIsomorphismFromInternalHomToTensorProduct
      1.7-8 TensorProductInternalHomCompatibilityMorphismInverse
      1.7-9 TensorProductInternalHomCompatibilityMorphismInverseWithGivenObjects
      1.7-10 AddTensorProductInternalHomCompatibilityMorphismInverseWithGivenObjects
      1.7-11 CoevaluationForDual
      1.7-12 CoevaluationForDualWithGivenTensorProduct
      1.7-13 AddCoevaluationForDualWithGivenTensorProduct
      1.7-14 TraceMap
      1.7-15 AddTraceMap
      1.7-16 RankMorphism
      1.7-17 AddRankMorphism
      1.7-18 MorphismFromBidual
      1.7-19 MorphismFromBidualWithGivenBidual
      1.7-20 AddMorphismFromBidualWithGivenBidual
    1.8 [33X[0;0YConvenience Methods[133X
      1.8-1 InternalHom
  
  
  [32X
