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Theorems · Definition · category theory

DerivedCategory.Q

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.Abelian C] →
      [inst_2 : HasDerivedCategory C] → CategoryTheory.Functor (CochainComplex C ℤ) (DerivedCategory C)

The localization functor CochainComplex C ℤ ⥤ DerivedCategory C.

Defined in
Mathlib.Algebra.Homology.DerivedCategory.Basic
Cited by
102 results in Mathlib
Foundations
Depth 99 from the axioms, rests on 2,201 definitions · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.AbelianHasDerivedCategory

Around this declaration

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

CategoryTheory.Abelian.Ext.comp_hom · cited by 27Ext.comp_homCategoryTheory.Abelian.Ext.mk₀_hom · cited by 20Ext.mk₀_homDerivedCategory.homologyFunctorFactors · cited by 20DerivedCategory.homologyF…DerivedCategory.triangleOfSES · cited by 17DerivedCategory.triangleO…DerivedCategory.quotientCompQhIso · cited by 16DerivedCategory.quotientC…CategoryTheory.Functor.mapDerivedCategorySingleFunctor · cited by 13Functor.mapDerivedCategor…DerivedCategory.TStructure.t · cited by 13TStructure.tDerivedCategory.singleFunctorIsoCompQ · cited by 10DerivedCategory.singleFun…CategoryTheory.Functor.mapDerivedCategoryFactors · cited by 10Functor.mapDerivedCategor…DerivedCategory.singleFunctorsPostcompQIso · cited by 9DerivedCategory.singleFun…CategoryTheory.Abelian.Ext.homEquiv · cited by 8Ext.homEquivDerivedCategory.triangleOfSESδ · cited by 8DerivedCategory.triangleO…CategoryTheory.ShortComplex.ShortExact.singleTriangleIso · cited by 7ShortExact.singleTriangle…DerivedCategory.homologyFunctorFactors_hom_naturality · cited by 6DerivedCategory.homologyF…CategoryTheory.ShortComplex.ShortExact.extClass_hom · cited by 6ShortExact.extClass_homCategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorCategoryTheory.Abelian · cited by 1753CategoryTheory.AbelianComplexShape.up · cited by 1123ComplexShape.upCochainComplex · cited by 1016CochainComplexHasDerivedCategory · cited by 190HasDerivedCategoryDerivedCategory · cited by 165DerivedCategoryHomologicalComplexUpToQuasiIso.Q · cited by 11HomologicalComplexUpToQua…DerivedCategory.QCITED BYCITES

Cites8

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

Cited by116

Results whose statement or proof uses this declaration.