Theorems · Definition · category theory

Homotopy.compLeftId

{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} →
            {f : D ⟶ D} →
              Homotopy f (CategoryTheory.CategoryStruct.id D) →
                (g : C ⟶ D) → Homotopy (CategoryTheory.CategoryStruct.comp g f) g

a variant of Homotopy.compLeft useful for dealing with homotopy equivalences.

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