Doi-Koppinen Hopf modules and entwined modules unify various kinds of
modules that have been intensively studied over the past decades, such
as Hopf modules, graded modules, Yetter-Drinfeld modules. The book
presents a unified theory, with focus on categorical concepts
generalizing the notions of separable and Frobenius algebras, and
discussing relations with smash products, Galois theory and descent
theory. Each chapter of Part II is devoted to a particular nonlinear
equation. The exposé is organized in such a way that the analogies
between the four are clear: the quantum Yang-Baxter equation is related
to Yetter-Drinfeld modules, the pentagon equation to Hopf modules, and
the Long equation to Long dimodules. The Frobenius-separability equation
provides a new viewpoint to Frobenius and separable algebras.