Weak \(C\)-cleft extensions, weak entwining structures and weak Hopf algebras.
The notion of weak entwining structures was introduced by \textit{S. Caenepeel} and \textit{E. De Groot} [Contemp. Math. 267, 31-54 (2000; Zbl 0978.16033)] generalizing previous work of Brzeziński and Majid. The importance of this notion is that it allows to unify the definition of several categories by putting them into the framework of `categories of entwined modules'. This paper introduces the notion of cleft extensions for weak entwining structures in a braided monoidal category with equalizers and coequalizers. It is shown that certain results in the literature, like for instance that of \textit{J. N. Alonso Álvarez} and \textit{R. González Rodríguez} [J. Algebra 281, No. 2, 731-752 (2004; Zbl 1073.16027)] on crossed products for weak Hopf algebras are particular instances of more general theorems that they obtain in the context of weak entwining structures.
scientific article; zbMATH DE number 2153321
scientific article