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FpCategories

Finitely presented categories by generating quivers and relations

2026.06-02

7 June 2026

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

2 Path categories

2.1 Constructors

  2.1-1 PathCategory
  2.1-2 ObjectConstructor
  2.1-3 MorphismConstructor
  2.1-4 AssignSetOfObjects
  2.1-5 AssignSetOfGeneratingMorphisms

  2.2-1 OppositePathCategory
  2.2-2 CategoryFromNerveData
  2.2-3 UnderlyingQuiver
  2.2-4 ObjectIndex
  2.2-5 ObjectLabel
  2.2-6 MorphismLength
  2.2-7 MorphismSupport
  2.2-8 MorphismIndices
  2.2-9 MorphismLabel
  2.2-10 IsFinitePathCategory
  2.2-11 HasFiniteNumberOfMacaulayMorphisms
  2.2-12 MacaulayMorphisms

2.3 GAP categories

  2.3-1 IsPathCategory
  2.3-2 IsPathCategoryObject
  2.3-3 IsPathCategoryMorphism

  2.4-1 GroebnerBasis
  2.4-2 ReducedGroebnerBasisWithGivenGroebnerBasis
  2.4-3 ReducedGroebnerBasis
  2.4-4 IsDescendingForMorphisms
  2.4-5 IsAscendingForMorphisms

3 Finite categories from data tables

  3.1-1 DataTables
  3.1-2 Size
  3.1-3 OppositeCategoryFromDataTables

3.2 Constructors

  3.2-1 CategoryFromDataTables
  3.2-2 CategoryFromDataTables
  3.2-3 CategoryFromDataTables
  3.2-4 CategoryFromDataTables
  3.2-5 CreateObject
  3.2-6 CreateMorphism

3.3 GAP categories

  3.3-1 IsCategoryFromDataTables
  3.3-2 IsCellInCategoryFromDataTables
  3.3-3 IsObjectInCategoryFromDataTables
  3.3-4 IsMorphismInCategoryFromDataTables

  4.2-1 DefiningTripleOfUnderlyingQuiver
  4.2-2 DataTablesOfCategory
  4.2-3 NerveTruncatedInDegree2Data
  4.2-4 NerveTruncatedInDegree2AsFunctor
  4.2-5 IndicesOfGeneratingMorphismsFromHomStructure
  4.2-6 OppositeFiniteCategory
  4.2-7 YonedaFibrationAsNaturalTransformation
  4.2-8 YonedaProjectionAsNaturalEpimorphism
  4.2-9 YonedaCompositionAsNaturalEpimorphism
  4.2-10 NaturalTransformation
  4.2-11 QuiverStringOfDigraph

5 Precompilation

5.1 PrecompileCategoryFromNerveData

5.2 PrecompileCategoryFromDataTables

6 Finite categories from nerve data

6.1 GAP categories

  6.1-1 IsCategoryFromNerveData
  6.1-2 IsObjectInCategoryFromNerveData
  6.1-3 IsMorphismInCategoryFromNerveData

  6.2-1 NerveData
  6.2-2 Size
  6.2-3 OppositeCategoryFromNerveData

6.3 Constructors

  6.3-1 CategoryFromNerveData
  6.3-2 CategoryFromNerveData
  6.3-3 CreateObject

7 Quotients of path categories

7.1 GAP categories

  7.1-1 IsQuotientOfPathCategory
  7.1-2 IsQuotientOfPathCategoryObject
  7.1-3 IsQuotientOfPathCategoryMorphism

  7.2-1 OppositeQuotientOfPathCategory
  7.2-2 CategoryFromNerveData
  7.2-3 DefiningRelations
  7.2-4 GroebnerBasisOfDefiningRelations
  7.2-5 ObjectIndex
  7.2-6 CanonicalRepresentative
  7.2-7 AssignSetOfObjects
  7.2-8 AssignSetOfGeneratingMorphisms

7.3 Constructors

7.3-1 QuotientCategory

8 Finitely presented categories generated by enhanced quivers

8.1 Global functions

8.1-1 SimplicialCategoryTruncatedInDegree

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