Theorems · Definition · category theory

HomotopyEquiv.refl

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

Any complex is homotopy equivalent to itself.

Defined in

Mathlib.Algebra.Homology.Homotopy

Cited by

4 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.Preadditive