Abstract
Let (A, B, D), (A′, B′, D′) be two triples consisting of a Hopf algebra A, an A-comodule algebra B and an A-module coalgebra D. Given α A → A′, β B → B′ and δ D → D′, we define an induction functor between the two corresponding categories of Doi-Koppinen Hopf smodules, and we prove that this functor has a right adjoint; this right adjoint is constructed using the cotensor product. We then investigate when this induction functor and its adjoint are inverse equivalences. We find a necessary and sufficient condition, which turns out to be of Galois-type in some special cases. To be able to prove our result, we have to introduce Doi-Koppinen Hopf bimodules and the bitensor product.
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