Morita Theory for corings and cleft entwining structures
  Using the theory of corings, we generalize and unify Morita contexts introduced by Chase and Sweedler, Doi, and Cohen, Fischman and Montgomery. We discuss when the contexts are strict. We apply our theory corings arising from entwining structures, and this leads us to the notion of cleft entwining structure. 
S. Caenepeel, J. Vercruysse and Shuanhong Wang