Theorems · Definition · category theory

CategoryTheory.Functor.mapHomotopy

{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] →
                      {f g : C ⟶ D} →
                        Homotopy f g → Homotopy ((F.mapHomologicalComplex c).map f) ((F.mapHomologicalComplex c).map g)

An additive functor takes homotopies to homotopies.

Defined in

Mathlib.Algebra.Homology.Homotopy

Cited by

3 results in Mathlib

Foundations

Depth 22 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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