Theorems · Definition · algebraic topology

AlgebraicTopology.DoldKan.homotopyEquivNormalizedMooreComplexAlternatingFaceMapComplex

{A : Type u_2} →
  [inst : CategoryTheory.Category.{v_2, u_2} A] →
    [inst_1 : CategoryTheory.Abelian A] →
      {Y : CategoryTheory.SimplicialObject A} →
        HomotopyEquiv ((AlgebraicTopology.normalizedMooreComplex A).obj Y)
          ((AlgebraicTopology.alternatingFaceMapComplex A).obj Y)

The inclusion of the Moore complex in the alternating face map complex is a homotopy equivalence

Defined in

Mathlib.AlgebraicTopology.DoldKan.HomotopyEquivalence

Cited by

4 results in Mathlib

Foundations

Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Abelian