Crossed products for weak Hopf algebras with coalgebra splitting. (Q1887484)

The main result of this paper is a generalization of the Blattner-Cohen-Montgomery Theorem [\textit{R. J. Blattner, M. Cohen} and \textit{S. Montgomery}, Trans. Am. Math. Soc. 298, 671-711 (1986; Zbl 0619.16004)] to weak Hopf algebras. A dual result can be shown in a similar way, and this leads to a generalization of \textit{D. E. Radford}'s Theorem [J. Algebra 92, 322-347 (1985; Zbl 0549.16003)] to weak Hopf algebras. The authors prove their results in arbitrary symmetric monoidal categories with split idempotents.