Theorems · Definition · category theory
HasDerivedCategory
(C : Type u) →
[inst : CategoryTheory.Category.{v, u} C] → [CategoryTheory.Abelian C] → Type (max (max ((max u v) + 1) v) (w + 1))The assumption that a localized category for
(HomologicalComplex.quasiIso C (ComplexShape.up ℤ)) has been chosen, and that the morphisms
in this chosen category are in Type w.
- Cited by
- 190 results in Mathlib
- Foundations
- Depth 94 from the axioms, rests on 2,187 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
- HomologicalComplex.quasiIsoproof · cited by 42
- CategoryTheory.MorphismProperty.HasLocalizationproof · cited by 15
Cited by242
Results whose statement or proof uses this declaration.
- DerivedCategorystatement and proof · cited by 165
- DerivedCategory.Qstatement and proof · cited by 102
- DerivedCategory.singleFunctorstatement and proof · cited by 78
- CategoryTheory.Abelian.Ext.homstatement and proof · cited by 42
- HasDerivedCategory.standardstatement · cited by 42
- DerivedCategory.homologyFunctorstatement and proof · cited by 35
- CategoryTheory.Abelian.Ext.extstatement and proof · cited by 31
- DerivedCategory.Qhstatement and proof · cited by 27
- CategoryTheory.Abelian.Ext.comp_homstatement and proof · cited by 27
- CategoryTheory.ShortComplex.ShortExact.singleTrianglestatement and proof · cited by 26
- CategoryTheory.HasExt.standardproof · cited by 22
- CategoryTheory.Abelian.Ext.mk₀_homstatement and proof · cited by 20
Showing the 200 most cited of 242.