Theorems · Definition · category theory

HomologicalComplexUpToQuasiIso.quotientCompQhIso

(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] →
              [inst_4 : c.QFactorsThroughHomotopy C] →
                (HomotopyCategory.quotient C c).comp HomologicalComplexUpToQuasiIso.Qh ≅
                  HomologicalComplexUpToQuasiIso.Q

The canonical isomorphism HomotopyCategory.quotient C c ⋙ Qh ≅ Q.

Defined in

Mathlib.Algebra.Homology.Localization

Cited by

7 results in Mathlib

Foundations

Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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