Theorems · Theorem · algebraic topology

CategoryTheory.SimplicialObject.Homotopy.congr_homologyMap_singularChainComplexFunctor

Deprecated since 2026-04-05Use CategoryTheory.SimplicialObject.Homotopy.congr_sSetHomologyMap instead.

∀ {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}
  [inst_3 : CategoryTheory.CategoryWithHomology C] (H : CategoryTheory.SimplicialObject.Homotopy f g) (R : C) (n : ℕ),
  SSet.homologyMap f R n = SSet.homologyMap g R n

Alias of CategoryTheory.SimplicialObject.Homotopy.congr_sSetHomologyMap. Simplicially homotopic maps of simplicial sets induce the same map on homology of the singular chain complex (with coefficients in R). The assumption is in SimplicialObject.Homotopy, see also SSet.Homotopy.congr_homologyMap for the variant using SSet.Homotopy as an assumption.

Defined in

Mathlib.AlgebraicTopology.SimplicialSet.Homology.HomotopyInvariance

Cited by

0 results in Mathlib

Foundations

Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveCategoryTheory.Limits.HasCoproductsCategoryTheory.CategoryWithHomology