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IntrinsicModules

Finitely presented modules over computable rings allowing multiple presentations and the notion of elements

2024.09-01

4 September 2024

Mohamed Barakat
Email: mohamed.barakat@uni-siegen.de
Homepage: https://mohamed-barakat.github.io/
Address:
Walter-Flex-Str. 3
57068 Siegen
Germany

Kamal Saleh
Email: kamal.saleh@uni-siegen.de
Homepage: https://github.com/kamalsaleh/
Address:
Walter-Flex-Str. 3
57068 Siegen
Germany

Contents

1 Categories of finitely presented modules

1.1 Constructors

  1.1-1 TurnAutoequivalenceIntoIdentityFunctorForHomalg
  1.1-2 CategoryOfHomalgFinitelyPresentedLeftModules
  1.1-3 CategoryOfHomalgFinitelyPresentedRightModules

1.2 Supported CAP operations

1.2-1 Category of finitely presented modules

1.3 Operations and global functions

  1.3-1 ImageEmbeddingForFpLeftModulesByFreyd
  1.3-2 ImageEmbeddingForFpRightModulesByFreyd
  1.3-3 ImageEmbeddingForFpLeftModulesByPresentations
  1.3-4 ImageEmbeddingForFpRightModulesByPresentations

1.4 GAP categories

1.4-1 IsCategoryOfHomalgModules

2.1 Constructors

2.1-1 HomalgRelationsForModule
2.1-2 HomalgRelationsForModule

3.1 Constructors

3.1-1 HomalgGeneratorsForModule

3.2-1 UpdateHomalgGenerators

4.1 Constructors

4.1-1 LeftPresentation
4.1-2 RightPresentation

5.1 Constructors

5.1-1 HomalgMap

6.1 Endofunctors of finitely presented modules

  6.1-1 FunctorStandardPresentationOfFpLeftModule
  6.1-2 FunctorStandardPresentationOfFpRightModule
  6.1-3 FunctorGetRidOfZeroGeneratorsOfFpLeftModule
  6.1-4 FunctorGetRidOfZeroGeneratorsOfFpRightModule
  6.1-5 FunctorLessGeneratorsOfLeftFpModule
  6.1-6 FunctorLessGeneratorsOfRightFpModule

7 Natural transformations

7.1 Natural isomorphisms from identity functor

  7.1-1 NaturalIsomorphismFromIdentityToStandardPresentationOfFpLeftModule
  7.1-2 NaturalIsomorphismFromIdentityToStandardPresentationOfFpRightModule
  7.1-3 NaturalIsomorphismFromIdentityToGetRidOfZeroGeneratorsOfFpLeftModule
  7.1-4 NaturalIsomorphismFromIdentityToGetRidOfZeroGeneratorsOfFpRightModule
  7.1-5 NaturalIsomorphismFromIdentityToLessGeneratorsOfFpLeftModule
  7.1-6 NaturalIsomorphismFromIdentityToLessGeneratorsOfFpRightModule

9 Examples and Tests

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