Theorems · Definition · category theory

CategoryTheory.Arrow.RightHomotopy.add

{V : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} V] →
    [inst_1 : CategoryTheory.Preadditive V] →
      {u v : CategoryTheory.Arrow V} →
        {f₁ g₁ f₂ g₂ : u ⟶ v} →
          CategoryTheory.Arrow.RightHomotopy f₁ g₁ →
            CategoryTheory.Arrow.RightHomotopy f₂ g₂ → CategoryTheory.Arrow.RightHomotopy (f₁ + f₂) (g₁ + g₂)

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

Defined in

Mathlib.CategoryTheory.Preadditive.FreydCategory.Homotopy

Cited by

1 results in Mathlib

Foundations

Depth 46 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Preadditive