Theorems · Definition · category theory

Homotopy.comp

{ι : Type u_1} →
  {V : Type u} →
    [inst : CategoryTheory.Category.{v, u} V] →
      [inst_1 : CategoryTheory.Preadditive V] →
        {c : ComplexShape ι} →
          {C₁ C₂ C₃ : HomologicalComplex V c} →
            {f₁ g₁ : C₁ ⟶ C₂} →
              {f₂ g₂ : C₂ ⟶ C₃} →
                Homotopy f₁ g₁ →
                  Homotopy f₂ g₂ →
                    Homotopy (CategoryTheory.CategoryStruct.comp f₁ f₂) (CategoryTheory.CategoryStruct.comp g₁ g₂)

homotopy is closed under composition

Defined in

Mathlib.Algebra.Homology.Homotopy

Cited by

1 results in Mathlib

Foundations

Depth 56 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Preadditive