ToolsForCategoricalTowers

Tools for CategoricalTowers

2024.04-01

22 April 2024

1 Tools

1.1 Tools

1.1-1 SET_RANGE_CATEGORY_Of_HOMOMORPHISM_STRUCTURE

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

Index

ToolsForCategoricalTowers

Tools for CategoricalTowers

Contents