Theorems · Definition · category theory

Homotopy.compLeft

{ι : Type u_1} →
  {V : Type u} →
    [inst : CategoryTheory.Category.{v, u} V] →
      [inst_1 : CategoryTheory.Preadditive V] →
        {c : ComplexShape ι} →
          {C D E : HomologicalComplex V c} →
            {f g : D ⟶ E} →
              Homotopy f g →
                (e : C ⟶ D) → Homotopy (CategoryTheory.CategoryStruct.comp e f) (CategoryTheory.CategoryStruct.comp e g)

homotopy is closed under composition (on the left)

Defined in

Mathlib.Algebra.Homology.Homotopy

Cited by

11 results in Mathlib

Foundations

Depth 22 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Preadditive