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ComplexesCategories

Category of (co)chain complexes of an additive category

2025.07-01

8 July 2025

Kamal Saleh
Email: kamal.saleh@uni-siegen.de
Homepage: https://github.com/kamalsaleh/
Address:
Walter-Flex-Str. 3
57068 Siegen
Germany

Contents

1.1 Constructing categories

  1.1-1 IsComplexesCategory
  1.1-2 IsComplexesCategoryByChains
  1.1-3 IsComplexesCategoryByCochains
  1.1-4 ComplexesCategoryByCochains
  1.1-5 ComplexesCategoryByChains
  1.1-6 UnderlyingCategory

1.2 Constructing objects

  1.2-1 IsChainOrCochainComplex
  1.2-2 IsChainComplex
  1.2-3 IsCochainComplex
  1.2-4 CreateComplex
  1.2-5 CreateComplex
  1.2-6 Objects
  1.2-7 ObjectAt
  1.2-8 \[\]
  1.2-9 Differentials
  1.2-10 DifferentialAt
  1.2-11 \^
  1.2-12 LowerBound
  1.2-13 UpperBound
  1.2-14 ObjectsSupport
  1.2-15 ObjectsSupport
  1.2-16 DifferentialsSupport
  1.2-17 DifferentialsSupport
  1.2-18 CocyclesAt
  1.2-19 CocyclesEmbeddingAt
  1.2-20 CoboundariesAt
  1.2-21 CoboundariesEmbeddingAt
  1.2-22 CohomologyAt
  1.2-23 CohomologySupport
  1.2-24 CohomologySupport
  1.2-25 CyclesAt
  1.2-26 CyclesEmbeddingAt
  1.2-27 BoundariesAt
  1.2-28 BoundariesEmbeddingAt
  1.2-29 HomologyAt
  1.2-30 HomologySupport
  1.2-31 HomologySupport
  1.2-32 IsExact
  1.2-33 IsExact
  1.2-34 AsChainComplex
  1.2-35 AsCochainComplex

2 Functors and natural transformations

  2.1-1 InclusionFunctorIntoComplexesCategoryByCochains
  2.1-2 InclusionFunctorIntoComplexesCategoryByChains
  2.1-3 ExtendFunctorToComplexesCategoriesByCochains
  2.1-4 ExtendFunctorToComplexesCategoriesByChains

2.2 Natural transformations

2.2-1 ExtendNaturalTransformationToComplexesCategoriesByChains
2.2-2 ExtendNaturalTransformationToComplexesCategoriesByCochains

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