Theorems · Definition · category theory

HomologicalComplexUpToQuasiIso.Qh

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    {ι : Type u_2} →
      {c : ComplexShape ι} →
        [inst_1 : CategoryTheory.Preadditive C] →
          [inst_2 : CategoryTheory.CategoryWithHomology C] →
            [inst_3 : (HomologicalComplex.quasiIso C c).HasLocalization] →
              [c.QFactorsThroughHomotopy C] →
                CategoryTheory.Functor (HomotopyCategory C c) (HomologicalComplexUpToQuasiIso C c)

The functor HomotopyCategory C c ⥤ HomologicalComplexUpToQuasiIso C c from the homotopy category to the localized category with respect to quasi-isomorphisms.

Defined in

Mathlib.Algebra.Homology.Localization

Cited by

8 results in Mathlib

Foundations

Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveCategoryTheory.CategoryWithHomologyCategoryTheory.MorphismProperty.HasLocalizationComplexShape.QFactorsThroughHomotopy