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ToolsForCategoricalTowers

Tools for CategoricalTowers

2025.06-02

12 June 2025

Mohamed Barakat
Email: mohamed.barakat@uni-siegen.de
Homepage: https://mohamed-barakat.github.io/
Address:
Walter-Flex-Str. 3
57068 Siegen
Germany

Contents

  1.1-1 SET_RANGE_CATEGORY_Of_HOMOMORPHISM_STRUCTURE
  1.1-2 ListKnownDoctrines
  1.1-3 DummyCategoryInDoctrines

1.2-1 CovariantHomFunctor
1.2-2 GlobalSectionFunctor

1.3 Cell as evaluatable string

1.3-1 DatumOfCellAsEvaluatableString
1.3-2 CellAsEvaluatableString

2 Futher CAP operations

2.1 MorphismBetweenCoproducts and MorphismBetweenDirectProducts

  2.1-1 MorphismBetweenCoproducts
  2.1-2 MorphismBetweenCoproductsWithGivenCoproducts
  2.1-3 MorphismBetweenDirectProducts
  2.1-4 MorphismBetweenDirectProductsWithGivenDirectProducts

2.2 Projective covers and injective envelopes

2.3 IsWeakTerminal and IsWeakInitial

2.3-1 IsWeakTerminal
2.3-2 IsWeakInitial

2.4 RelativeLift/RelativeColift

2.4-1 RelativeLift

2.5 Biased relative weak fiber product

  2.5-1 BiasedRelativeWeakFiberProduct
  2.5-2 ProjectionOfBiasedRelativeWeakFiberProduct
  2.5-3 ProjectionOfBiasedRelativeWeakFiberProductWithGivenBiasedRelativeWeakFiberProduct
  2.5-4 UniversalMorphismIntoBiasedRelativeWeakFiberProduct
  2.5-5 UniversalMorphismIntoBiasedRelativeWeakFiberProductWithGivenBiasedRelativeWeakFiberProduct

2.6 EmbeddingOfSumOfImagesOfAllMorphisms

  2.6-1 MorphismOntoSumOfImagesOfAllMorphisms
  2.6-2 EmbeddingOfSumOfImagesOfAllMorphisms
  2.6-3 SumOfImagesOfAllMorphisms

2.7 Systems of homogeneous linear equations in linear categories

  2.8-1 LimitPair
  2.8-2 Limit
  2.8-3 ProjectionInFactorOfLimit
  2.8-4 ProjectionInFactorOfLimitWithGivenLimit
  2.8-5 UniversalMorphismIntoLimit
  2.8-6 UniversalMorphismIntoLimitWithGivenLimit

  2.9-1 ColimitPair
  2.9-2 Colimit
  2.9-3 InjectionOfCofactorOfColimit
  2.9-4 InjectionOfCofactorOfColimitWithGivenColimit
  2.9-5 UniversalMorphismFromColimit
  2.9-6 UniversalMorphismFromColimitWithGivenColimit
  2.9-7 PositionsOfSublist
  2.9-8 AllCoproducts

2.10 Add-methods

  2.10-1 AddBiasedRelativeWeakFiberProduct
  2.10-2 AddColimit
  2.10-3 AddEmbeddingOfSumOfImagesOfAllMorphisms
  2.10-4 AddInjectionOfCofactorOfColimit
  2.10-5 AddInjectionOfCofactorOfColimitWithGivenColimit
  2.10-6 AddIsWeakInitial
  2.10-7 AddIsWeakTerminal
  2.10-8 AddLimit
  2.10-9 AddMorphismBetweenCoproducts
  2.10-10 AddMorphismBetweenCoproductsWithGivenCoproducts
  2.10-11 AddMorphismBetweenDirectProducts
  2.10-12 AddMorphismBetweenDirectProductsWithGivenDirectProducts
  2.10-13 AddMorphismOntoSumOfImagesOfAllMorphisms
  2.10-14 AddProjectionInFactorOfLimit
  2.10-15 AddProjectionInFactorOfLimitWithGivenLimit
  2.10-16 AddProjectionOfBiasedRelativeWeakFiberProduct
  2.10-17 AddProjectionOfBiasedRelativeWeakFiberProductWithGivenBiasedRelativeWeakFiberProduct
  2.10-18 AddRelativeLift
  2.10-19 AddSumOfImagesOfAllMorphisms
  2.10-20 AddUniversalMorphismFromColimit
  2.10-21 AddUniversalMorphismFromColimitWithGivenColimit
  2.10-22 AddUniversalMorphismIntoBiasedRelativeWeakFiberProduct
  2.10-23 AddUniversalMorphismIntoBiasedRelativeWeakFiberProductWithGivenBiasedRelativeWeakFiberProduct
  2.10-24 AddUniversalMorphismIntoLimit
  2.10-25 AddUniversalMorphismIntoLimitWithGivenLimit

3 ToolsForCategoricalTowers automatic generated documentation

3.1 ToolsForCategoricalTowers automatic generated documentation of global functions

3.1-1 DigraphOfKnownDoctrines

3.2 ToolsForCategoricalTowers automatic generated documentation of methods

3.2-1 Visualize

3.3 ToolsForCategoricalTowers automatic generated documentation of attributes

3.3-1 SvgString

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