Theorems · Definition · category theory

Homotopy.trans

{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} → {e f g : C ⟶ D} → Homotopy e f → Homotopy f g → Homotopy e g

homotopy is a transitive relation.

Defined in

Mathlib.Algebra.Homology.Homotopy

Cited by

18 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.Preadditive