Theorems · Definition · category theory

CategoryTheory.Functor.mapHomotopyEquiv

{ι : Type u_1} →
  {V : Type u} →
    [inst : CategoryTheory.Category.{v, u} V] →
      [inst_1 : CategoryTheory.Preadditive V] →
        {c : ComplexShape ι} →
          {C D : HomologicalComplex V c} →
            {W : Type u_2} →
              [inst_2 : CategoryTheory.Category.{v_1, u_2} W] →
                [inst_3 : CategoryTheory.Preadditive W] →
                  (F : CategoryTheory.Functor V W) →
                    [inst_4 : F.Additive] →
                      HomotopyEquiv C D →
                        HomotopyEquiv ((F.mapHomologicalComplex c).obj C) ((F.mapHomologicalComplex c).obj D)

An additive functor preserves homotopy equivalences.

Defined in

Mathlib.Algebra.Homology.Homotopy

Cited by

4 results in Mathlib

Foundations

Depth 23 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveCategoryTheory.CategoryCategoryTheory.PreadditiveCategoryTheory.Functor.Additive