A Maschke type theorem for weak group entwined modules and applications

The Morita contexts and galois extensions for weak Hopf group coalgebras

“…The axioms are the same as ones for Hopf algebras, but the multiplicativity of the counit and comultiplicativity of the unit are replaced by weaker axioms. These naturally lead to the introduction of weak Hopf algebras in Turaev module category called weak Hopf group coalgebras in [9][10][11][12].…”

Ribbon entwining datum

“…Note that the definition of entwined modules generalizes lots of important modules such as Hopf modules, Doi-Hopf modules, and Yetter-Drinfel'd modules ( [9], [17]). Further researches on entwining structures can be found in [1], [21], [23], and so on.…”