Theorems · Definition · category theory
DerivedCategory
(C : Type u) →
[inst : CategoryTheory.Category.{v, u} C] →
[inst_1 : CategoryTheory.Abelian C] → [HasDerivedCategory C] → Type (max u v)The derived category of an abelian category.
- Cited by
- 165 results in Mathlib
- Foundations
- Depth 95 from the axioms, rests on 2,191 definitions · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement and proof · cited by 32,673
- CategoryTheory.Abelianstatement and proof · cited by 1,753
- ComplexShape.upproof · cited by 1,123
- HasDerivedCategorystatement and proof · cited by 190
- HomologicalComplexUpToQuasiIsoproof · cited by 12
Cited by211
Results whose statement or proof uses this declaration.
- DerivedCategory.Qstatement · cited by 102
- DerivedCategory.singleFunctorstatement · cited by 78
- CategoryTheory.Abelian.Ext.homstatement · cited by 42
- DerivedCategory.homologyFunctorstatement · cited by 35
- CategoryTheory.Abelian.Ext.extstatement · cited by 31
- DerivedCategory.Qhstatement · cited by 27
- CategoryTheory.Abelian.Ext.comp_homstatement · cited by 27
- CategoryTheory.ShortComplex.ShortExact.singleTrianglestatement · cited by 26
- CategoryTheory.Abelian.Ext.mk₀_homstatement · cited by 20
- DerivedCategory.homologyFunctorFactorsstatement · cited by 20
- CategoryTheory.Functor.mapDerivedCategorystatement · cited by 18
- DerivedCategory.triangleOfSESstatement · cited by 17
Showing the 200 most cited of 211.