  
  
                          [1X ModulePresentationsForCAP [101X
  
  
                           [1X Category R-pres for CAP [101X
  
  
                                   2022.12-01
  
  
                                14 December 2022
  
  
                               Sebastian Gutsche
  
                                Sebastian Posur
  
  
  
  Sebastian Gutsche
      Email:    [7Xmailto:gutsche@mathematik.uni-siegen.de[107X
      Homepage: [7Xhttps://sebasguts.github.io/[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: [7Xhttps://sebastianpos.github.io[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 (ModulePresentationsForCAP)[101X
  
  1 [33X[0;0YModule Presentations[133X
    1.1 [33X[0;0YFunctors[133X
      1.1-1 FunctorStandardModuleLeft
      1.1-2 FunctorStandardModuleRight
      1.1-3 FunctorGetRidOfZeroGeneratorsLeft
      1.1-4 FunctorGetRidOfZeroGeneratorsRight
      1.1-5 FunctorLessGeneratorsLeft
      1.1-6 FunctorLessGeneratorsRight
      1.1-7 FunctorDualLeft
      1.1-8 FunctorDualRight
      1.1-9 FunctorDoubleDualLeft
      1.1-10 FunctorDoubleDualRight
    1.2 [33X[0;0YGAP Categories[133X
      1.2-1 IsLeftOrRightPresentationMorphism
      1.2-2 IsLeftPresentationMorphism
      1.2-3 IsRightPresentationMorphism
      1.2-4 IsLeftOrRightPresentation
      1.2-5 IsLeftPresentation
      1.2-6 IsRightPresentation
    1.3 [33X[0;0YConstructors[133X
      1.3-1 PresentationMorphism
      1.3-2 AsMorphismBetweenFreeLeftPresentations
      1.3-3 AsMorphismBetweenFreeRightPresentations
      1.3-4 AsLeftPresentation
      1.3-5 AsRightPresentation
      1.3-6 AsLeftOrRightPresentation
      1.3-7 FreeLeftPresentation
      1.3-8 FreeRightPresentation
      1.3-9 UnderlyingMatrix
      1.3-10 UnderlyingHomalgRing
      1.3-11 Annihilator
      1.3-12 LeftPresentationsAsFreydCategoryOfCategoryOfRows
      1.3-13 RightPresentationsAsFreydCategoryOfCategoryOfColumns
      1.3-14 LeftPresentations
      1.3-15 RightPresentations
    1.4 [33X[0;0YAttributes[133X
      1.4-1 UnderlyingHomalgRing
      1.4-2 UnderlyingMatrix
    1.5 [33X[0;0YNon-Categorical Operations[133X
      1.5-1 StandardGeneratorMorphism
      1.5-2 CoverByFreeModule
    1.6 [33X[0;0YNatural Transformations[133X
      1.6-1 NaturalIsomorphismFromIdentityToStandardModuleLeft
      1.6-2 NaturalIsomorphismFromIdentityToStandardModuleRight
      1.6-3 NaturalIsomorphismFromIdentityToGetRidOfZeroGeneratorsLeft
      1.6-4 NaturalIsomorphismFromIdentityToGetRidOfZeroGeneratorsRight
      1.6-5 NaturalIsomorphismFromIdentityToLessGeneratorsLeft
      1.6-6 NaturalIsomorphismFromIdentityToLessGeneratorsRight
      1.6-7 NaturalTransformationFromIdentityToDoubleDualLeft
      1.6-8 NaturalTransformationFromIdentityToDoubleDualRight
  2 [33X[0;0YExamples and Tests[133X
    2.1 [33X[0;0YAnnihilator[133X
    2.2 [33X[0;0YIntersection of Submodules[133X
    2.3 [33X[0;0YKoszul Complex[133X
    2.4 [33X[0;0YClosed Monoidal Structure[133X
    2.5 [33X[0;0YProjectivity test[133X
  
  
  [32X
