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ModulePresentationsForCAP

Category R-pres for CAP

2018.02.02

2 February 2018

Sebastian Gutsche
Email: 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: sebastian.posur@uni-siegen.de
Homepage: https://sebastianpos.github.io
Address:
Department Mathematik
Universität Siegen
Walter-Flex-Straße 3
57068 Siegen
Germany

Contents

1 Module Presentations

  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

1.4-1 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

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