Theorems · Definition · category theory
DerivedCategory.Qh
{C : Type u} →
[inst : CategoryTheory.Category.{v, u} C] →
[inst_1 : CategoryTheory.Abelian C] →
[inst_2 : HasDerivedCategory C] →
CategoryTheory.Functor (HomotopyCategory C (ComplexShape.up ℤ)) (DerivedCategory C)The localization functor HomotopyCategory C (ComplexShape.up ℤ) ⥤ DerivedCategory C.
- Cited by
- 27 results in Mathlib
- Foundations
- Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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.Functorstatement · cited by 16,252
- CategoryTheory.Abelianstatement and proof · cited by 1,753
- ComplexShape.upstatement · cited by 1,123
- HasDerivedCategorystatement and proof · cited by 190
- DerivedCategorystatement · cited by 165
- HomotopyCategorystatement · cited by 132
- HomologicalComplexUpToQuasiIso.Qhproof · cited by 8
Cited by35
Results whose statement or proof uses this declaration.
- DerivedCategory.quotientCompQhIsostatement · cited by 16
- DerivedCategory.singleFunctorsproof · cited by 13
- DerivedCategory.homologyFunctorFactorshstatement · cited by 9
- DerivedCategory.singleFunctorsPostcompQIsoproof · cited by 9
- DerivedCategory.isIso_Qh_map_iffstatement and proof · cited by 3
- CochainComplex.IsKInjective.Qh_map_bijectivestatement and proof · cited by 3
- DerivedCategory.homologyFunctorFactorsh_hom_app_quotient_objstatement · cited by 2
- DerivedCategory.homologyFunctorFactorsh_inv_app_quotient_objstatement · cited by 2
- DerivedCategory.mem_distTriang_iffproof · cited by 2
- DerivedCategory.quotientCompQhIso_hom_naturality_assocstatement and proof · cited by 2
- DerivedCategory.quotientCompQhIso_inv_naturalitystatement · cited by 2
- DerivedCategory.shiftMap_homologyFunctor_map_Qproof · cited by 2