A functor from simplicial algebras to crossed \( n \)-cubes is shown to be an embedding on a reflexive subcategory of the category of simplicial algebras that contains representatives for all \( n \) types.
ARVASİ, Z. and KOÇAK, M. (1998) "Dold-Kan Type Theorems for n-Types of Simplicitial Commutative Algebras," Turkish Journal of Mathematics: Vol. 22: No. 2, Article 5. Available at: https://journals.tubitak.gov.tr/math/vol22/iss2/5