Theorems · Definition · category theory

Homotopy.nullHomotopy

{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} →
            (hom : (i j : ι) → C.X i ⟶ D.X j) →
              (∀ (i j : ι), ¬c.Rel j i → hom i j = 0) → Homotopy (Homotopy.nullHomotopicMap hom) 0

Tautological construction of the Homotopy to zero for maps constructed by nullHomotopicMap, at least when we have the zero condition.

Defined in

Mathlib.Algebra.Homology.Homotopy

Cited by

1 results in Mathlib

Foundations

Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Preadditive