Theorems · Definition · category theory

HomotopyCategory.isoOfHomotopyEquiv

{ι : Type u_2} →
  {V : Type u} →
    [inst : CategoryTheory.Category.{v, u} V] →
      [inst_1 : CategoryTheory.Preadditive V] →
        {c : ComplexShape ι} →
          {C D : HomologicalComplex V c} →
            HomotopyEquiv C D → ((HomotopyCategory.quotient V c).obj C ≅ (HomotopyCategory.quotient V c).obj D)

Homotopy equivalent complexes become isomorphic in the homotopy category.

Defined in

Mathlib.Algebra.Homology.HomotopyCategory

Cited by

4 results in Mathlib

Foundations

Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Preadditive