Theorems · Definition · category theory

Homotopy.toShortComplex

{C : Type u_2} →
  [inst : CategoryTheory.Category.{v_1, u_2} C] →
    [inst_1 : CategoryTheory.Preadditive C] →
      {ι : Type u_3} →
        {c : ComplexShape ι} →
          [DecidableRel c.Rel] →
            {K L : HomologicalComplex C c} →
              {f g : K ⟶ L} →
                Homotopy f g →
                  (i : ι) →
                    CategoryTheory.ShortComplex.Homotopy ((HomologicalComplex.shortComplexFunctor C c i).map f)
                      ((HomologicalComplex.shortComplexFunctor C c i).map g)

A homotopy between morphisms of homological complexes K ⟶ L induces a homotopy between morphisms of short complexes K.sc i ⟶ L.sc i.

Defined in

Mathlib.Algebra.Homology.Homotopy

Cited by

1 results in Mathlib

Foundations

Depth 40 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveDecidableRel