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SliceCategories

Slice categories

2026.04-01

24 April 2026

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

Contents

1 Slice categories
 1.1 GAP categories

  1.1-1 IsSliceCategory
  1.1-2 IsCellInASliceCategory
  1.1-3 IsObjectInASliceCategory
  1.1-4 IsMorphismInASliceCategory
  1.1-5 IsSliceCategoryOverTensorUnit
  1.1-6 IsCellInSliceCategoryOverTensorUnit
  1.1-7 IsObjectInSliceCategoryOverTensorUnit
  1.1-8 IsMorphismInSliceCategoryOverTensorUnit
 1.2 Global variables

  1.2-1 CAP_INTERNAL_METHOD_NAME_LIST_FOR_SLICE_CATEGORY
 1.3 Attributes

  1.3-1 AmbientCategory
  1.3-2 BaseObject
  1.3-3 BaseObject
  1.3-4 UnderlyingMorphism
  1.3-5 SourceOfUnderlyingMorphism
  1.3-6 UnderlyingCell
  1.3-7 InclusionFunctor
  1.3-8 DualOverTensorUnit
 1.4 Constructors

  1.4-1 AsSliceCategoryCell
  1.4-2 /
  1.4-3 AsSliceCategoryCell
 1.5 Operations

  1.5-1 MorphismFromCovariantArgumentOfInternalHom
2 Slice categories (eager data structure)
 2.1 GAP categories

  2.1-1 IsEagerSliceCategory
  2.1-2 IsCellInAnEagerSliceCategory
  2.1-3 IsObjectInAnEagerSliceCategory
  2.1-4 IsMorphismInAnEagerSliceCategory
  2.1-5 IsEagerSliceCategoryOverTensorUnit
  2.1-6 IsCellInAnEagerSliceCategoryOverTensorUnit
  2.1-7 IsObjectInAnEagerSliceCategoryOverTensorUnit
  2.1-8 IsMorphismInAnEagerSliceCategoryOverTensorUnit
 2.2 Constructors

  2.2-1 SliceCategory
  2.2-2 SliceCategoryOverTensorUnit
  2.2-3 AsSliceCategoryCell
 2.3 Examples

  2.3-1 SliceCategory
  2.3-2 SliceCategoryOverTensorUnit
  2.3-3 IteratedInternalHom
  2.3-4 Double pushout rewriting
  2.3-5 Precompilation
3 Slice categories (lazy data structure)
 3.1 GAP categories

  3.1-1 IsLazySliceCategory
  3.1-2 IsCellInALazySliceCategory
  3.1-3 IsObjectInALazySliceCategory
  3.1-4 IsMorphismInALazySliceCategory
  3.1-5 IsLazySliceCategoryOverTensorUnit
  3.1-6 IsCellInALazySliceCategoryOverTensorUnit
  3.1-7 IsObjectInALazySliceCategoryOverTensorUnit
  3.1-8 IsMorphismInALazySliceCategoryOverTensorUnit
 3.2 Attributes

  3.2-1 UnderlyingMorphismList
 3.3 Constructors

  3.3-1 LazySliceCategory
  3.3-2 LazySliceCategoryOverTensorUnit
  3.3-3 AsSliceCategoryCell
 3.4 Examples

  3.4-1 LazySliceCategory
Index

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