Frobenius and separable functors for the category of entwined modules   over cowreaths, I: General theory
  Entwined modules over cowreaths in a monoidal category are introduced. They can be identified to coalgebras in an appropriate monoidal category. It is investigated when such coalgebras are Frobenius (resp. separable), and when the forgetful functor from entwined modules to representations of the underlying algebra is Frobenius (resp. separable). These properties are equivalent when the unit object of the category is a $\otimes$-generator. 
D. Bulacu, S. Caenepeel and B. Torrecillas
math.CT