  
  
                              [1X MonoidalCategories [101X
  
  
                 [1X Monoidal and monoidal (co)closed categories [101X
  
  
                                   2019.06.07
  
  
                                  7 June 2019
  
  
                                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;0YTensor Product and Internal Hom[133X
    1.1 [33X[0;0YMonoidal Categories[133X
      1.1-1 TensorProductOnObjects
      1.1-2 AddTensorProductOnObjects
      1.1-3 TensorProductOnMorphisms
      1.1-4 TensorProductOnMorphismsWithGivenTensorProducts
      1.1-5 AddTensorProductOnMorphismsWithGivenTensorProducts
      1.1-6 AssociatorRightToLeft
      1.1-7 AssociatorRightToLeftWithGivenTensorProducts
      1.1-8 AddAssociatorRightToLeftWithGivenTensorProducts
      1.1-9 AssociatorLeftToRight
      1.1-10 AssociatorLeftToRightWithGivenTensorProducts
      1.1-11 AddAssociatorLeftToRightWithGivenTensorProducts
      1.1-12 TensorUnit
      1.1-13 AddTensorUnit
      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
      1.1-26 LeftDistributivityExpanding
      1.1-27 LeftDistributivityExpandingWithGivenObjects
      1.1-28 AddLeftDistributivityExpandingWithGivenObjects
      1.1-29 LeftDistributivityFactoring
      1.1-30 LeftDistributivityFactoringWithGivenObjects
      1.1-31 AddLeftDistributivityFactoringWithGivenObjects
      1.1-32 RightDistributivityExpanding
      1.1-33 RightDistributivityExpandingWithGivenObjects
      1.1-34 AddRightDistributivityExpandingWithGivenObjects
      1.1-35 RightDistributivityFactoring
      1.1-36 RightDistributivityFactoringWithGivenObjects
      1.1-37 AddRightDistributivityFactoringWithGivenObjects
    1.2 [33X[0;0YBraided Monoidal Categories[133X
      1.2-1 Braiding
      1.2-2 BraidingWithGivenTensorProducts
      1.2-3 AddBraidingWithGivenTensorProducts
      1.2-4 BraidingInverse
      1.2-5 BraidingInverseWithGivenTensorProducts
      1.2-6 AddBraidingInverseWithGivenTensorProducts
    1.3 [33X[0;0YSymmetric Monoidal Categories[133X
    1.4 [33X[0;0YSymmetric Closed Monoidal Categories[133X
      1.4-1 InternalHomOnObjects
      1.4-2 AddInternalHomOnObjects
      1.4-3 InternalHomOnMorphisms
      1.4-4 InternalHomOnMorphismsWithGivenInternalHoms
      1.4-5 AddInternalHomOnMorphismsWithGivenInternalHoms
      1.4-6 EvaluationMorphism
      1.4-7 EvaluationMorphismWithGivenSource
      1.4-8 AddEvaluationMorphismWithGivenSource
      1.4-9 CoevaluationMorphism
      1.4-10 CoevaluationMorphismWithGivenRange
      1.4-11 AddCoevaluationMorphismWithGivenRange
      1.4-12 TensorProductToInternalHomAdjunctionMap
      1.4-13 AddTensorProductToInternalHomAdjunctionMap
      1.4-14 InternalHomToTensorProductAdjunctionMap
      1.4-15 AddInternalHomToTensorProductAdjunctionMap
      1.4-16 MonoidalPreComposeMorphism
      1.4-17 MonoidalPreComposeMorphismWithGivenObjects
      1.4-18 AddMonoidalPreComposeMorphismWithGivenObjects
      1.4-19 MonoidalPostComposeMorphism
      1.4-20 MonoidalPostComposeMorphismWithGivenObjects
      1.4-21 AddMonoidalPostComposeMorphismWithGivenObjects
      1.4-22 DualOnObjects
      1.4-23 AddDualOnObjects
      1.4-24 DualOnMorphisms
      1.4-25 DualOnMorphismsWithGivenDuals
      1.4-26 AddDualOnMorphismsWithGivenDuals
      1.4-27 EvaluationForDual
      1.4-28 EvaluationForDualWithGivenTensorProduct
      1.4-29 AddEvaluationForDualWithGivenTensorProduct
      1.4-30 CoevaluationForDual
      1.4-31 CoevaluationForDualWithGivenTensorProduct
      1.4-32 AddCoevaluationForDualWithGivenTensorProduct
      1.4-33 MorphismToBidual
      1.4-34 MorphismToBidualWithGivenBidual
      1.4-35 AddMorphismToBidualWithGivenBidual
      1.4-36 TensorProductInternalHomCompatibilityMorphism
      1.4-37 TensorProductInternalHomCompatibilityMorphismWithGivenObjects
      1.4-38 AddTensorProductInternalHomCompatibilityMorphismWithGivenObjects
      1.4-39 TensorProductDualityCompatibilityMorphism
      1.4-40 TensorProductDualityCompatibilityMorphismWithGivenObjects
      1.4-41 AddTensorProductDualityCompatibilityMorphismWithGivenObjects
      1.4-42 MorphismFromTensorProductToInternalHom
      1.4-43 MorphismFromTensorProductToInternalHomWithGivenObjects
      1.4-44 AddMorphismFromTensorProductToInternalHomWithGivenObjects
      1.4-45 IsomorphismFromTensorProductToInternalHom
      1.4-46 AddIsomorphismFromTensorProductToInternalHom
      1.4-47 MorphismFromInternalHomToTensorProduct
      1.4-48 MorphismFromInternalHomToTensorProductWithGivenObjects
      1.4-49 AddMorphismFromInternalHomToTensorProductWithGivenObjects
      1.4-50 IsomorphismFromInternalHomToTensorProduct
      1.4-51 AddIsomorphismFromInternalHomToTensorProduct
      1.4-52 TraceMap
      1.4-53 AddTraceMap
      1.4-54 RankMorphism
      1.4-55 AddRankMorphism
      1.4-56 IsomorphismFromDualToInternalHom
      1.4-57 AddIsomorphismFromDualToInternalHom
      1.4-58 IsomorphismFromInternalHomToDual
      1.4-59 AddIsomorphismFromInternalHomToDual
      1.4-60 UniversalPropertyOfDual
      1.4-61 AddUniversalPropertyOfDual
      1.4-62 LambdaIntroduction
      1.4-63 AddLambdaIntroduction
      1.4-64 LambdaElimination
      1.4-65 AddLambdaElimination
      1.4-66 IsomorphismFromObjectToInternalHom
      1.4-67 IsomorphismFromObjectToInternalHomWithGivenInternalHom
      1.4-68 AddIsomorphismFromObjectToInternalHomWithGivenInternalHom
      1.4-69 IsomorphismFromInternalHomToObject
      1.4-70 IsomorphismFromInternalHomToObjectWithGivenInternalHom
      1.4-71 AddIsomorphismFromInternalHomToObjectWithGivenInternalHom
    1.5 [33X[0;0YRigid Symmetric Closed Monoidal Categories[133X
      1.5-1 TensorProductInternalHomCompatibilityMorphismInverse
      1.5-2 TensorProductInternalHomCompatibilityMorphismInverseWithGivenObjects
      1.5-3 AddTensorProductInternalHomCompatibilityMorphismInverseWithGivenObjects
      1.5-4 MorphismFromBidual
      1.5-5 MorphismFromBidualWithGivenBidual
      1.5-6 AddMorphismFromBidualWithGivenBidual
  2 [33X[0;0YExamples and Tests[133X
    2.1 [33X[0;0YBasics[133X
  
  
  [32X
