Pivotal and Ribbon Entwining Datums
  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. 
Xiaohui Zhang, Wei Wang, Xiaofan Zhao
math.RA math.QA