Abstract
We give the necessary and sufficient conditions for a family of Brzezínski crossed product algebras with suitable comultiplication and counit to be a Hopf π-coalgebra. On the other hand, necessary and sufficient conditions for the Brzeziński π-crossed product A⧫H to be a coquasitriangular Hopf π-coalgebra are derived, then the category A⧫H ℳ of the left π-comodules over A⧫H is braided.
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