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DerivedCategories

Derived categories of Abelian categories

2022.10-03

24 October 2022

Kamal Saleh
Email: kamal.saleh@uni-siegen.de
Homepage: https://github.com/kamalsaleh
Address:
Department Mathematik
Universität Siegen
Walter-Flex-Straße 3
57068 Siegen
Germany

Contents

1 Exceptional collections

1.1 Constructors

  1.1-1 IsStrongExceptionalCollection
  1.1-2 CreateStrongExceptionalCollection
  1.1-3 StrongExceptionalCollection
  1.1-4 FullSubcategory
  1.1-5 AmbientCategory
  1.1-6 EndomorphismAlgebraAttr
  1.1-7 EndomorphismAlgebra
  1.1-8 DefiningStrongExceptionalCollection
  1.1-9 Algebroid
  1.1-10 QuiverRows
  1.1-11 TiltingObject
  1.1-12 NumberOfObjects
  1.1-13 UnderlyingObjects
  1.1-14 AdditiveClosure
  1.1-15 CategoryOfQuiverRepresentationsOverOppositeAlgebra
  1.1-16 HomotopyCategory
  1.1-17 AdditiveClosureAsFullSubcategory
  1.1-18 \[\]
  1.1-19 PathsOfLengthGreaterThanOne
  1.1-20 PathsOfLengthOne
  1.1-21 Arrows
  1.1-22 AllPaths
  1.1-23 BasisOfPaths
  1.1-24 LabelsForPathsOfLengthOne
  1.1-25 LabelsForPathsOfLengthGreaterThanOne
  1.1-26 LabelsForAllPaths
  1.1-27 LabelsForBasisOfPaths

1.2 General Operations

  1.2-1 InterpretListOfMorphismsAsOneMorphismInRangeCategoryOfHomomorphismStructure
  1.2-2 RandomQuiverAlgebraWhoseIndecProjectiveRepsAreStrongExceptionalCollection
  1.2-3 RelationsBetweenMorphisms
  1.2-4 FullSubcategoryGeneratedByProjectiveObjects
  1.2-5 FullSubcategoryGeneratedByInjectiveObjects
  1.2-6 FullSubcategoryGeneratedByIndecProjectiveObjects
  1.2-7 FullSubcategoryGeneratedByIndecInjectiveObjects
  1.2-8 AdditiveClosureAsFullSubcategory

2 Functors and natural transformations

  2.1-1 DecompositionFunctorOfProjectiveQuiverRepresentations
  2.1-2 QuasiInverseOfDecompositionFunctorOfProjectiveQuiverRepresentations
  2.1-3 DecompositionFunctorOfInjectiveQuiverRepresentations
  2.1-4 QuasiInverseOfDecompositionFunctorOfInjectiveQuiverRepresentations
  2.1-5 IsomorphismOntoAlgebroid
  2.1-6 IsomorphismFromAlgebroid
  2.1-7 YonedaIsomorphismOntoFullSubcategoryOfCategoryOfQuiverRepresentations
  2.1-8 YonedaIsomorphismOntoFullSubcategoryOfCategoryOfQuiverRepresentations
  2.1-9 InverseOfYonedaIsomorphismOntoFullSubcategoryOfCategoryOfQuiverRepresentations
  2.1-10 InverseOfYonedaIsomorphismOntoFullSubcategoryOfCategoryOfQuiverRepresentations
  2.1-11 LocalizationFunctor
  2.1-12 UniversalFunctorFromDerivedCategory
  2.1-13 LeftDerivedFunctor
  2.1-14 RightDerivedFunctor
  2.1-15 TensorFunctorFromCategoryOfQuiverRepresentations
  2.1-16 TensorFunctorFromCategoryOfQuiverRepresentationsOnIndecProjectiveObjects
  2.1-17 TensorFunctorFromCategoryOfQuiverRepresentationsOnProjectiveObjects

2.2 Natural transformations

2.2-1 UnitOfTensorHomAdjunction
2.2-2 CounitOfTensorHomAdjunction

3 DerivedCategories automatic generated documentation

3.1 DerivedCategories automatic generated documentation of attributes

  3.1-1 HomFunctorToCategoryOfQuiverRepresentations
  3.1-2 HomFunctorToCategoryOfQuiverRepresentationsOnIndecInjectiveObjects
  3.1-3 HomFunctorToCategoryOfQuiverRepresentationsOnInjectiveObjects

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