In this work, we give a characterization of free crossed modules and also get a relation between projective crossed modules and the cyclic homology of associative algebras by using Hopf-type formulas.
"Projective crossed modules of algebras and cyclic homology,"
Turkish Journal of Mathematics: Vol. 40:
5, Article 6.
Available at: https://journals.tubitak.gov.tr/math/vol40/iss5/6