Theorems · Definition · category theory

CategoryTheory.Functor.mapHomologicalComplexUpToQuasiIsoLocalizerMorphism

{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 : F.Additive] →
                        [F.PreservesHomology] →
                          CategoryTheory.LocalizerMorphism (HomologicalComplex.quasiIso C c)
                            (HomologicalComplex.quasiIso D c)

The localizer morphism which expresses that F.mapHomologicalComplex c preserves quasi-isomorphisms.

Defined in

Mathlib.Algebra.Homology.Localization

Cited by

5 results in Mathlib

Foundations

Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.PreadditiveCategoryTheory.PreadditiveCategoryTheory.CategoryWithHomologyCategoryTheory.CategoryWithHomologyCategoryTheory.Functor.AdditiveCategoryTheory.Functor.PreservesHomology