Theorems · Inductive type · category theory

HomotopyEquiv

{ι : Type u_1} →
  {V : Type u} →
    [inst : CategoryTheory.Category.{v, u} V] →
      [inst_1 : CategoryTheory.Preadditive V] →
        {c : ComplexShape ι} → HomologicalComplex V c → HomologicalComplex V c → Type (max u_1 v)

A homotopy equivalence between two chain complexes consists of a chain map each way, and homotopies from the compositions to the identity chain maps. Note that this contains data; arguably it might be more useful for many applications if we truncated it to a Prop.

Defined in

Mathlib.Algebra.Homology.Homotopy

Cited by

27 results in Mathlib

Foundations

Depth 18 from the axioms · uses propext

Assumes

CategoryTheory.CategoryCategoryTheory.Preadditive