Theorems · Definition · category theory

HomotopyEquiv.copy

{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} → (f : HomotopyEquiv C D) → {g : C ⟶ D} → Homotopy f.hom g → HomotopyEquiv C D

If f if a homotopy equivalence and h is a homotopy from f.hom to a morphism g, then this is a homotopy equivalence whose hom field is g.

Defined in

Mathlib.Algebra.Homology.Homotopy

Cited by

3 results in Mathlib

Foundations

Depth 56 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Preadditive