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Published online by Cambridge University Press: 21 February 2019
We introduce the category of two-sided two-cosided Hopf modules over a quasi-bialgebra H and show that it is braided monoidally equivalent to the category of Yetter–Drinfeld modules over H, provided that H is a quasi-Hopf algebra. We use this equivalence to obtain structure theorems for bicomodule algebras and bimodule coalgebras over H. Finally, we show that a Hopf algebra within this braided monoidal category identifies with a quasi-Hopf algebra with projection.
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