Theorems · Definition · category theory

CategoryTheory.Functor.mapHomologicalComplexUpToQuasiIsoFactorsh

{C : Type u_1} →
  {D : Type u_2} →
    [inst : CategoryTheory.Category.{v_1, u_1} C] →
      [inst_1 : CategoryTheory.Category.{v_2, u_2} D] →
        (F : CategoryTheory.Functor C D) →
          {ι : Type u_3} →
            (c : ComplexShape ι) →
              [inst_2 : CategoryTheory.Preadditive C] →
                [inst_3 : CategoryTheory.Preadditive D] →
                  [inst_4 : CategoryTheory.CategoryWithHomology C] →
                    [inst_5 : CategoryTheory.CategoryWithHomology D] →
                      [inst_6 : (HomologicalComplex.quasiIso D c).HasLocalization] →
                        [inst_7 : F.Additive] →
                          [inst_8 : F.PreservesHomology] →
                            [inst_9 : (HomologicalComplex.quasiIso C c).HasLocalization] →
                              [inst_10 : c.QFactorsThroughHomotopy C] →
                                [inst_11 : c.QFactorsThroughHomotopy D] →
                                  [(HomotopyCategory.quotient C c).IsLocalization
                                        (HomologicalComplex.homotopyEquivalences C c)] →
                                    HomologicalComplexUpToQuasiIso.Qh.comp (F.mapHomologicalComplexUpToQuasiIso c) ≅
                                      (F.mapHomotopyCategory c).comp HomologicalComplexUpToQuasiIso.Qh

The functor F.mapHomologicalComplexUpToQuasiIso c is induced by F.mapHomotopyCategory c.

Defined in

Mathlib.Algebra.Homology.Localization

Cited by

3 results in Mathlib

Foundations

Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.PreadditiveCategoryTheory.PreadditiveCategoryTheory.CategoryWithHomologyCategoryTheory.CategoryWithHomologyCategoryTheory.MorphismProperty.HasLocalizationCategoryTheory.Functor.AdditiveCategoryTheory.Functor.PreservesHomologyCategoryTheory.MorphismProperty.HasLocalizationComplexShape.QFactorsThroughHomotopyComplexShape.QFactorsThroughHomotopyCategoryTheory.Functor.IsLocalization