Smash (co)Products and skew pairings

Abstract

Let t be an invertible skew pairing on (B,H) where B and H are Hopf algebras in a symmetric monoidal category C with (co)equalizers. Assume that H is quasitriangular. Then we obtain a new algebra structure such that B is a Hopf algebra in the braided category HH?D and there exists a Hopf algebra isomorphism w: B 8 H ? B [×]t H in C, where B 8 H is a Hopf algebra with (co)algebra structure the smash (co)product and B [×]t H is the Hopf algebra defined by Doi and Takeuchi.