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FpCategories

Finitely presented categories by generating quivers and relations

2024.04-02

22 April 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 Quivers
 1.1 GAP categories

  1.1-1 IsFinQuiver
  1.1-2 IsFinQuiverObject
  1.1-3 IsFinQuiverMorphism
 1.2 Constructors

  1.2-1 FinQuiver
  1.2-2 ObjectConstructor
  1.2-3 MorphismConstructor
  1.2-4 RandomFinQuiver
  1.2-5 TensorProductOfFinQuivers
 1.3 Attributes

  1.3-1 QuiverDatum
  1.3-2 QuiverName
  1.3-3 NumberOfObjects
  1.3-4 LabelsOfObjects
  1.3-5 LaTeXStringsOfObjects
  1.3-6 NumberOfMorphisms
  1.3-7 LabelsOfMorphisms
  1.3-8 LaTeXStringsOfMorphisms
  1.3-9 IndicesOfSources
  1.3-10 IndicesOfTargets
  1.3-11 IndicesPairsOfCompatibleMorphisms
  1.3-12 SetOfObjects
  1.3-13 SetOfMorphisms
  1.3-14 ExternalHoms
  1.3-15 OppositeQuiver
  1.3-16 ObjectIndex
  1.3-17 ObjectLabel
  1.3-18 UnderlyingFinQuiver
  1.3-19 MorphismIndex
  1.3-20 MorphismLabel
  1.3-21 UnderlyingFinQuiver
2 Path Categories
 2.1 GAP categories

  2.1-1 IsPathCategory
  2.1-2 IsPathCategoryObject
  2.1-3 IsPathCategoryMorphism
 2.2 Constructors

  2.2-1 PathCategory
  2.2-2 ObjectConstructor
  2.2-3 MorphismConstructor
  2.2-4 AssignSetOfObjects
  2.2-5 AssignSetOfGeneratingMorphisms
 2.3 Attributes

  2.3-1 UnderlyingQuiver
  2.3-2 ObjectIndex
  2.3-3 ObjectLabel
  2.3-4 MorphismLength
  2.3-5 MorphismSupport
  2.3-6 MorphismIndices
  2.3-7 MorphismLabel
  2.3-8 IsFinitePathCategory
  2.3-9 HasFiniteNumberOfMacaulayMorphisms
  2.3-10 MacaulayMorphisms
 2.4 Operations

  2.4-1 GroebnerBasis
  2.4-2 ReducedGroebnerBasisWithGivenGroebnerBasis
  2.4-3 ReducedGroebnerBasis
  2.4-4 IsDescendingForMorphisms
  2.4-5 IsAscendingForMorphisms
 2.5 Quotients of path categories

  2.5-1 IsQuotientOfPathCategory
  2.5-2 IsQuotientOfPathCategoryObject
  2.5-3 IsQuotientOfPathCategoryMorphism
  2.5-4 QuotientCategory
  2.5-5 DefiningRelations
  2.5-6 GroebnerBasisOfDefiningRelations
  2.5-7 ObjectIndex
  2.5-8 CanonicalRepresentative
3 Tools
 3.1 Properties

  3.1-1 IsFinitelyPresentedCategory
 3.2 Operations

  3.2-1 DefiningTripleOfUnderlyingQuiver
  3.2-2 DataTablesOfCategory
  3.2-3 QuiverStringOfDigraph
 3.3 Attributes

  3.3-1 SetOfGeneratingMorphismsOfCategory
  3.3-2 SetOfGeneratingMorphisms
4 Futher CAP operations
 4.1 Add-methods

  4.1-1 AddSetOfGeneratingMorphismsOfCategory
Index

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