Duality Theorem and Drinfeld Double in Braided Tensor Categories

Let $H$ be a finite Hopf algebra with $C_{H,H}=C_{H,H}^{-1}\mathrm{.}$ The duality theorem is shown for $H$, i.e., (R # H)# H^{\hat *} \cong R \otimes (H \bar \otimes H^{\hat *}) \hbox {as algebras in} {\cal C}. Also, it is proved that the Drinfeld double $(D(H),[b])$ is a quasi-triangular Hopf algebra in ${\cal C}$.