# Commit 2022-08-31 11:42 f951e201

View on Github →feat(algebraic_topology/dold_kan): the normalized Moore complex is homotopy equivalent to the alternating face map complex (#16246)
In this PR, when the category `A`

is abelian, we obtain the homotopy equivalence `homotopy_equiv_normalized_Moore_complex_alternating_face_map_complex`

between the normalized Moore complex and the alternating face map complex of a simplicial object in `A`

.