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IntrinsicGradedModules

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

2024.09-02

6 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 graded modules

1.1 Constructors

  1.1-1 LeftPresentationWithDegrees
  1.1-2 RightPresentationWithDegrees
  1.1-3 CategoryOfHomalgFinitelyPresentedGradedLeftModules
  1.1-4 CategoryOfHomalgFinitelyPresentedGradedRightModules

  1.2-1 FunctorStandardGradedModuleLeft
  1.2-2 FunctorStandardGradedModuleRight
  1.2-3 FunctorGetRidOfZeroHomogeneousGeneratorsLeft
  1.2-4 FunctorGetRidOfZeroHomogeneousGeneratorsRight
  1.2-5 FunctorLessHomogeneousGeneratorsLeft
  1.2-6 FunctorLessHomogeneousGeneratorsRight
  1.2-7 FunctorGradedDualLeft
  1.2-8 FunctorGradedDualRight
  1.2-9 FunctorDoubleGradedDualLeft
  1.2-10 FunctorDoubleGradedDualRight

1.3 Natural transformations

  1.3-1 NaturalIsomorphismFromIdentityToStandardGradedModuleLeft
  1.3-2 NaturalIsomorphismFromIdentityToStandardGradedModuleRight
  1.3-3 NaturalIsomorphismFromIdentityToGetRidOfZeroHomogeneousGeneratorsLeft
  1.3-4 NaturalIsomorphismFromIdentityToGetRidOfZeroHomogeneousGeneratorsRight
  1.3-5 NaturalIsomorphismFromIdentityToLessHomogeneousGeneratorsLeft
  1.3-6 NaturalIsomorphismFromIdentityToLessHomogeneousGeneratorsRight
  1.3-7 NaturalTransformationFromIdentityToDoubleGradedDualLeft
  1.3-8 NaturalTransformationFromIdentityToDoubleGradedDualRight

1.5 Supported CAP operations

1.5-1 Category of of finitely presented graded modules

1.6 GAP categories

1.6-1 IsCategoryOfHomalgGradedModules

2 Examples and Tests

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