Theorems · Definition · category theory

Homotopy.equivSubZero

{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 g : C ⟶ D} → Homotopy f g ≃ Homotopy (f - g) 0

f is homotopic to g iff f - g is homotopic to 0.

Defined in

Mathlib.Algebra.Homology.Homotopy

Cited by

3 results in Mathlib

Foundations

Depth 23 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Preadditive