Theorems · Definition · algebraic topology

CategoryTheory.SimplicialObject.Homotopy.sSetChainComplexMap

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.Preadditive C] →
      [inst_2 : CategoryTheory.Limits.HasCoproducts C] →
        {X Y : SSet} →
          {f g : X ⟶ Y} →
            CategoryTheory.SimplicialObject.Homotopy f g →
              (R : C) → Homotopy (SSet.chainComplexMap f R) (SSet.chainComplexMap g R)

If f and g are simplicially homotopic maps of simplicial sets, then they induce chain-homotopic maps on the singular chain complexes with coefficients in R. The assumption is in SimplicialObject.Homotopy, see also SSet.Homotopy.chainComplexMap for the variant using SSet.Homotopy as an assumption.

Defined in

Mathlib.AlgebraicTopology.SimplicialSet.Homology.HomotopyInvariance

Cited by

1 results in Mathlib

Foundations

Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveCategoryTheory.Limits.HasCoproducts