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SubcategoriesForCAP

Subcategory and other related constructors for CAP categories

2024.04-02

24 April 2024

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

Tom Kuhmichel
Email: tom.kuhmichel@student.uni-siegen.de
Homepage: https://github.com/TKuh
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
57072 Siegen
Germany

Contents

1 Subcategories

1.1 GAP categories

  1.1-1 IsCapSubcategory
  1.1-2 IsCapSubcategoryGeneratedByFiniteNumberOfMorphisms
  1.1-3 IsCellInASubcategory
  1.1-4 IsObjectInASubcategory
  1.1-5 IsMorphismInASubcategory

1.2 Global variables

1.2-1 CAP_INTERNAL_METHOD_NAME_LIST_FOR_SUBCATEGORY

  1.3-1 UnderlyingCell
  1.3-2 SetOfKnownObjects
  1.3-3 AmbientCategory

1.4 Constructors

  1.4-1 Subcategory
  1.4-2 AsSubcategoryCell
  1.4-3 AsSubcategoryCell
  1.4-4 \/
  1.4-5 SubcategoryGeneratedByListOfMorphisms

2 Full subcategories

2.1 GAP categories

  2.1-1 IsCapFullSubcategory
  2.1-2 IsCapFullSubcategoryGeneratedByFiniteNumberOfObjects
  2.1-3 IsCapFullSubcategoryDefinedByObjectMembershipFunction
  2.1-4 IsCellInAFullSubcategory
  2.1-5 IsObjectInAFullSubcategory
  2.1-6 IsMorphismInAFullSubcategory

2.2 Global variables

2.2-1 CAP_INTERNAL_METHOD_NAME_LIST_FOR_FULL_SUBCATEGORY
2.2-2 CAP_INTERNAL_METHOD_NAME_LIST_FOR_ADDITIVE_FULL_SUBCATEGORY

2.3 Constructors

  2.3-1 FullSubcategory
  2.3-2 FullSubcategoryGeneratedByListOfObjects
  2.3-3 FullSubcategoryOfIndecomposableProjectiveObjects
  2.3-4 FullSubcategoryOfIndecomposableInjectiveObjects
  2.3-5 FullSubcategoryByObjectMembershipFunction
  2.3-6 FullSubcategoryOfProjectiveObjects
  2.3-7 FullSubcategoryOfInjectiveObjects

  2.4-1 InclusionFunctor
  2.4-2 RestrictFunctorToFullSubcategoryOfSource
  2.4-3 RestrictFunctorToFullSubcategoryOfRange
  2.4-4 RestrictFunctorToFullSubcategories

3 Slice categories

3.1 GAP categories

  3.1-1 IsSliceCategory
  3.1-2 IsCellInASliceCategory
  3.1-3 IsObjectInASliceCategory
  3.1-4 IsMorphismInASliceCategory
  3.1-5 IsSliceCategoryOverTensorUnit
  3.1-6 IsCellInSliceCategoryOverTensorUnit
  3.1-7 IsObjectInSliceCategoryOverTensorUnit
  3.1-8 IsMorphismInSliceCategoryOverTensorUnit

3.2 Global variables

3.2-1 CAP_INTERNAL_METHOD_NAME_LIST_FOR_SLICE_CATEGORY

  3.3-1 AmbientCategory
  3.3-2 BaseObject
  3.3-3 BaseObject
  3.3-4 UnderlyingMorphism
  3.3-5 SourceOfUnderlyingMorphism
  3.3-6 UnderlyingCell
  3.3-7 InclusionFunctor
  3.3-8 DualOverTensorUnit

3.4 Constructors

  3.4-1 AsSliceCategoryCell
  3.4-2 /
  3.4-3 AsSliceCategoryCell

3.5-1 MorphismFromCovariantArgumentOfInternalHom

5 Slice categories (lazy data structure)

5.1 GAP categories

  5.1-1 IsLazySliceCategory
  5.1-2 IsCellInALazySliceCategory
  5.1-3 IsObjectInALazySliceCategory
  5.1-4 IsMorphismInALazySliceCategory
  5.1-5 IsLazySliceCategoryOverTensorUnit
  5.1-6 IsCellInALazySliceCategoryOverTensorUnit
  5.1-7 IsObjectInALazySliceCategoryOverTensorUnit
  5.1-8 IsMorphismInALazySliceCategoryOverTensorUnit

5.2-1 UnderlyingMorphismList

5.3 Constructors

  5.3-1 LazySliceCategory
  5.3-2 LazySliceCategoryOverTensorUnit
  5.3-3 AsSliceCategoryCell

5.4-1 LazySliceCategory

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