Theorems · Inductive type · category theory

Homotopy

{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} → (C ⟶ D) → (C ⟶ D) → Type (max u_1 v)

A homotopy h between chain maps f and g consists of components h i j : C.X i ⟶ D.X j which are zero unless c.Rel j i, satisfying the homotopy condition.

Defined in

Mathlib.Algebra.Homology.Homotopy

Cited by

106 results in Mathlib

Foundations

Depth 18 from the axioms, rests on 198 definitions · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Preadditive