  Dual monoidal category $\mathcal C^\ast$ of a monoidal functor $F:\mathcal
C\to \mathcal V$ has been constructed by S. Majid. In this paper, we extend the
construction of dual structures for an Ann-functor $F:\mathcal B\to \mathcal
A$. In particular, when $F=id_{\mathcal A}$, then the dual category $\mathcal
A^{\ast}$ is indeed the center of $\mathcal A$ and this is a braided
Ann-category.
