ModulePresentationsForCAP 
  
  
                            Category R-pres for CAP 
  
  
                                   2017.09.09
  
  
                                9 September 2017
  
  
                               Sebastian Gutsche
  
                                Sebastian Posur
  
  
  
  Sebastian Gutsche
      Email:    mailto:gutsche@mathematik.uni-siegen.de
      Homepage: http://www.uni-siegen.de/fb6/rmi/
      Address:  Department Mathematik
                Universität Siegen
                Walter-Flex-Straße 3
                57068 Siegen
                Germany
  
  
  Sebastian Posur
      Email:    mailto:sebastian.posur@uni-siegen.de
      Homepage: http://www.uni-siegen.de/fb6/rmi/
      Address:  Department Mathematik
                Universität Siegen
                Walter-Flex-Straße 3
                57068 Siegen
                Germany
  
  
  
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  Contents (ModulePresentationsForCAP)
  
  1 Module Presentations
    1.1 Functors
      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 GAP Categories
      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 Constructors
      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 LeftPresentations
      1.3-13 RightPresentations
    1.4 Attributes
      1.4-1 UnderlyingHomalgRing
      1.4-2 UnderlyingMatrix
    1.5 Non-Categorical Operations
      1.5-1 StandardGeneratorMorphism
      1.5-2 CoverByFreeModule
    1.6 Natural Transformations
      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 Examples and Tests
    2.1 Annihilator
    2.2 Intersection of Submodules
    2.3 Koszul Complex
    2.4 Closed Monoidal Structure