  In this paper we introduce the theory of multiplication alteration by
two-cocycles for nonassociative structures like nonassociative bimonoids with
left (right) division. Also we explore the connections between Yetter-Drinfeld
modules for Hopf quasigroups, projections of Hopf quasigroups, skew pairings,
and quasitriangular structures, obtaining the nonassociative version of the
main results proved by Doi and Takeuchi for Hopf algebras.
