Mathlib Map

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.

Defined in
Mathlib.Algebra.Homology.DerivedCategory.Basic
Cited by
27 results in Mathlib
Foundations
Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.AbelianHasDerivedCategory

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

DerivedCategory.quotientCompQhIso · cited by 16DerivedCategory.quotientC…DerivedCategory.singleFunctors · cited by 13DerivedCategory.singleFun…DerivedCategory.homologyFunctorFactorsh · cited by 9DerivedCategory.homologyF…DerivedCategory.singleFunctorsPostcompQIso · cited by 9DerivedCategory.singleFun…DerivedCategory.isIso_Qh_map_iff · cited by 3DerivedCategory.isIso_Qh_…CochainComplex.IsKInjective.Qh_map_bijective · cited by 3IsKInjective.Qh_map_bijec…DerivedCategory.homologyFunctorFactorsh_hom_app_quotient_obj · cited by 2DerivedCategory.homologyF…DerivedCategory.homologyFunctorFactorsh_inv_app_quotient_obj · cited by 2DerivedCategory.homologyF…DerivedCategory.mem_distTriang_iff · cited by 2DerivedCategory.mem_distT…DerivedCategory.quotientCompQhIso_hom_naturality_assoc · cited by 2DerivedCategory.quotientC…DerivedCategory.quotientCompQhIso_inv_naturality · cited by 2DerivedCategory.quotientC…DerivedCategory.shiftMap_homologyFunctor_map_Q · cited by 2DerivedCategory.shiftMap_…DerivedCategory.shiftMap_homologyFunctor_map_Qh · cited by 2DerivedCategory.shiftMap_…DerivedCategory.singleFunctorsPostcompQIso_hom_hom · cited by 2DerivedCategory.singleFun…DerivedCategory.singleFunctorsPostcompQIso_inv_hom · cited by 2DerivedCategory.singleFun…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorCategoryTheory.Abelian · cited by 1753CategoryTheory.AbelianComplexShape.up · cited by 1123ComplexShape.upHasDerivedCategory · cited by 190HasDerivedCategoryDerivedCategory · cited by 165DerivedCategoryHomotopyCategory · cited by 132HomotopyCategoryHomologicalComplexUpToQuasiIso.Qh · cited by 8HomologicalComplexUpToQua…DerivedCategory.QhCITED BYCITES

Cites8

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by35

Results whose statement or proof uses this declaration.