Hopf–Galois systems

We introduce the concept of Hopf–Galois system, a reformulation of the notion of Galois extension of the base field for a Hopf algebra. The main feature of our definition is a generalization of the antipode of an ordinary Hopf algebra. We present several examples which indicate that although our axiomatic is slightly more complicated than the classical one, it is also more natural and easier to handle with. The main application of Hopf–Galois systems is the construction of monoidal equivalences between comodule categories.