GAP (ModulePresentationsForCAP) - Contents

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# ModulePresentationsForCAP

## Category R-pres for CAP

2015.12.09

09/12/2015

Sebastian Gutsche
Email: gutsche@mathematik.uni-kl.de
Homepage: http://wwwb.math.rwth-aachen.de/~gutsche/
Address:
Department of Mathematics
University of Kaiserslautern
67653 Kaiserslautern
Germany

Sebastian Posur
Email: sposur@momo.math.rwth-aachen.de
Homepage: http://wwwb.math.rwth-aachen.de/Mitarbeiter/posur.php
Address:
Lehrstuhl B für Mathematik RWTH - Aachen
Templergraben 64
52062 Aachen
Germany

### Contents

1 Module Presentations
1.1 Functors
1.1-1 FunctorStandardModuleLeft
1.1-2 FunctorStandardModuleRight
1.1-3 FunctorLessGeneratorsLeft
1.1-4 FunctorLessGeneratorsRight
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 AsLeftPresentation
1.3-3 AsRightPresentation
1.3-4 AsLeftOrRightPresentation
1.3-5 FreeLeftPresentation
1.3-6 FreeRightPresentation
1.3-7 UnderlyingMatrix
1.3-8 UnderlyingHomalgRing
1.3-9 LeftPresentations
1.3-10 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
2 Examples and Tests
2.1 Intersection of Submodules
2.2 Koszul Complex
2.3 Closed Monoidal Structure
Index
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