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ToolsForCategoricalTowers

Tools for CategoricalTowers

2025.05-02

31 May 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 Tools
 1.1 Tools

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

  1.2-1 IsObjectFiniteCategory
  1.2-2 IsFiniteCategory
  1.2-3 IsEquivalentToFiniteCategory
 1.3 Attributes

  1.3-1 SetOfObjectsOfCategory
  1.3-2 SetOfObjects
  1.3-3 SetOfMorphismsOfFiniteCategory
  1.3-4 SetOfMorphisms
 1.4 Functors

  1.4-1 CovariantHomFunctor
  1.4-2 GlobalSectionFunctor
 1.5 Cell as evaluatable string

  1.5-1 DatumOfCellAsEvaluatableString
  1.5-2 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

  2.7-1 MereExistenceOfUniqueSolutionOfLinearSystemInAbCategory
  2.7-2 MereExistenceOfUniqueSolutionOfHomogeneousLinearSystemInAbCategory
  2.7-3 BasisOfSolutionsOfHomogeneousLinearSystemInLinearCategory
  2.7-4 BasisOfSolutionsOfHomogeneousDoubleLinearSystemInLinearCategory
  2.7-5 BasisOfSolutionsOfHomogeneousDoubleLinearSystemInLinearCategory
 2.8 Limit

  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 Colimit

  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 AddBasisOfSolutionsOfHomogeneousDoubleLinearSystemInLinearCategory
  2.10-2 AddBasisOfSolutionsOfHomogeneousLinearSystemInLinearCategory
  2.10-3 AddBiasedRelativeWeakFiberProduct
  2.10-4 AddColimit
  2.10-5 AddEmbeddingOfSumOfImagesOfAllMorphisms
  2.10-6 AddInjectionOfCofactorOfColimit
  2.10-7 AddInjectionOfCofactorOfColimitWithGivenColimit
  2.10-8 AddIsWeakInitial
  2.10-9 AddIsWeakTerminal
  2.10-10 AddLimit
  2.10-11 AddMereExistenceOfUniqueSolutionOfHomogeneousLinearSystemInAbCategory
  2.10-12 AddMereExistenceOfUniqueSolutionOfLinearSystemInAbCategory
  2.10-13 AddMorphismBetweenCoproducts
  2.10-14 AddMorphismBetweenCoproductsWithGivenCoproducts
  2.10-15 AddMorphismBetweenDirectProducts
  2.10-16 AddMorphismBetweenDirectProductsWithGivenDirectProducts
  2.10-17 AddMorphismOntoSumOfImagesOfAllMorphisms
  2.10-18 AddProjectionInFactorOfLimit
  2.10-19 AddProjectionInFactorOfLimitWithGivenLimit
  2.10-20 AddProjectionOfBiasedRelativeWeakFiberProduct
  2.10-21 AddProjectionOfBiasedRelativeWeakFiberProductWithGivenBiasedRelativeWeakFiberProduct
  2.10-22 AddRelativeLift
  2.10-23 AddSetOfMorphismsOfFiniteCategory
  2.10-24 AddSetOfObjectsOfCategory
  2.10-25 AddSumOfImagesOfAllMorphisms
  2.10-26 AddUniversalMorphismFromColimit
  2.10-27 AddUniversalMorphismFromColimitWithGivenColimit
  2.10-28 AddUniversalMorphismIntoBiasedRelativeWeakFiberProduct
  2.10-29 AddUniversalMorphismIntoBiasedRelativeWeakFiberProductWithGivenBiasedRelativeWeakFiberProduct
  2.10-30 AddUniversalMorphismIntoLimit
  2.10-31 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
Index

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