  Let $(C,A,\varphi)$ be an entwining structure over $k$. In this paper, we
introduce the notions of the pivotal entwined datums and ribbon entwined datums
to generalize (co)pivotal Hopf algebras and (co)ribbon Hopf algebras. These
notions give necessary and sufficient conditions for the category of entwined
modules to be a pivotal category and ribbon category.
