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FpCategories

Finitely presented categories by generating quivers and relations

2024.10-02

30 October 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 Constructors

  1.1-1 FinQuiver
  1.1-2 ObjectConstructor
  1.1-3 MorphismConstructor
  1.1-4 RandomFinQuiver
  1.1-5 TensorProductOfFinQuivers
 1.2 Attributes

  1.2-1 QuiverDatum
  1.2-2 QuiverName
  1.2-3 NumberOfObjects
  1.2-4 LabelsOfObjects
  1.2-5 LaTeXStringsOfObjects
  1.2-6 NumberOfMorphisms
  1.2-7 LabelsOfMorphisms
  1.2-8 LaTeXStringsOfMorphisms
  1.2-9 IndicesOfSources
  1.2-10 IndicesOfTargets
  1.2-11 IndicesPairsOfCompatibleMorphisms
  1.2-12 SetOfObjects
  1.2-13 SetOfMorphisms
  1.2-14 ExternalHoms
  1.2-15 OppositeQuiver
  1.2-16 ObjectIndex
  1.2-17 ObjectLabel
  1.2-18 UnderlyingFinQuiver
  1.2-19 MorphismIndex
  1.2-20 MorphismLabel
  1.2-21 UnderlyingFinQuiver
 1.3 GAP categories

  1.3-1 IsFinQuiver
  1.3-2 IsFinQuiverObject
  1.3-3 IsFinQuiverMorphism
2 Path categories
 2.1 Constructors

  2.1-1 QuotientCategory
 2.2 Attributes

  2.2-1 OppositeQuotientOfPathCategory
  2.2-2 CategoryFromNerveData
  2.2-3 DefiningRelations
  2.2-4 GroebnerBasisOfDefiningRelations
  2.2-5 ObjectIndex
  2.2-6 CanonicalRepresentative
 2.3 GAP categories

  2.3-1 IsQuotientOfPathCategory
  2.3-2 IsQuotientOfPathCategoryObject
  2.3-3 IsQuotientOfPathCategoryMorphism
3 Tools
 3.1 Properties

  3.1-1 IsFinitelyPresentedCategory
 3.2 Attributes

  3.2-1 SetOfGeneratingMorphismsOfCategory
  3.2-2 SetOfGeneratingMorphisms
  3.2-3 Size
 3.3 Operations

  3.3-1 DefiningTripleOfUnderlyingQuiver
  3.3-2 DataTablesOfCategory
  3.3-3 NerveTruncatedInDegree2Data
  3.3-4 NerveTruncatedInDegree2AsFunctor
  3.3-5 IndicesOfGeneratingMorphismsFromHomStructure
  3.3-6 OppositeFiniteCategory
  3.3-7 YonedaFibrationAsNaturalTransformation
  3.3-8 YonedaProjectionAsNaturalEpimorphism
  3.3-9 YonedaCompositionAsNaturalEpimorphism
  3.3-10 NaturalTransformation
  3.3-11 QuiverStringOfDigraph
4 Precompilation
5 Finite categories from nerve data
 5.1 GAP categories

  5.1-1 IsCategoryFromNerveData
  5.1-2 IsCellInCategoryFromNerveData
  5.1-3 IsObjectInCategoryFromNerveData
  5.1-4 IsMorphismInCategoryFromNerveData
 5.2 Attributes

  5.2-1 NerveData
  5.2-2 Size
  5.2-3 OppositeCategoryFromNerveData
 5.3 Constructors

  5.3-1 CategoryFromNerveData
  5.3-2 CategoryFromNerveData
  5.3-3 CreateObject
  5.3-4 CreateMorphism
6 Path Categories
 6.1 Operations

  6.1-1 GroebnerBasis
  6.1-2 ReducedGroebnerBasisWithGivenGroebnerBasis
  6.1-3 ReducedGroebnerBasis
  6.1-4 IsDescendingForMorphisms
  6.1-5 IsAscendingForMorphisms
 6.2 GAP categories

  6.2-1 IsPathCategory
  6.2-2 IsPathCategoryObject
  6.2-3 IsPathCategoryMorphism
 6.3 Constructors

  6.3-1 PathCategory
  6.3-2 ObjectConstructor
  6.3-3 MorphismConstructor
  6.3-4 AssignSetOfObjects
  6.3-5 AssignSetOfGeneratingMorphisms
 6.4 Attributes

  6.4-1 OppositePathCategory
  6.4-2 CategoryFromNerveData
  6.4-3 UnderlyingQuiver
  6.4-4 ObjectIndex
  6.4-5 ObjectLabel
  6.4-6 MorphismLength
  6.4-7 MorphismSupport
  6.4-8 MorphismIndices
  6.4-9 MorphismLabel
  6.4-10 IsFinitePathCategory
  6.4-11 HasFiniteNumberOfMacaulayMorphisms
  6.4-12 MacaulayMorphisms
7 Finitely presented categories generated by enhanced quivers
 7.1 Global functions

  7.1-1 SimplicialCategoryTruncatedInDegree
8 Futher CAP operations
 8.1 Add-methods

  8.1-1 AddSetOfGeneratingMorphismsOfCategory
Index

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