Theorems · Definition · category theory

Homotopy.add

{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} →
            {f₁ g₁ f₂ g₂ : C ⟶ D} → Homotopy f₁ g₁ → Homotopy f₂ g₂ → Homotopy (f₁ + f₂) (g₁ + g₂)

the sum of two homotopies is a homotopy between the sum of the respective morphisms.

Defined in

Mathlib.Algebra.Homology.Homotopy

Cited by

3 results in Mathlib

Foundations

Depth 55 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Preadditive