Weak Bialgebras and Monoidal Categories

Abstract

Abstract We study monoidal structures on the category of (co)modules over a weak bialgebra. Results due to Nill and Szlachányi are unified and extended to infinite algebras. We discuss the coalgebra structure on the source and target space of a weak bialgebra. Key Words: Monoidal categoryWeak bialgebra2010 Mathematics Subject Classification: 16T05 ACKNOWLEDGMENTS The first named author was supported by the Hungarian Scientific Research Fund OTKA K68195. The second and third named authors were supported by the research project G.0117.10 "Equivariant Brauer groups and Galois deformations" from FWO-Vlaanderen. All authors wish to thank Joost Vercruysse for fruitful discussions. Notes Communicated by S. Montgomery. To Mia Cohen, on the occasion of her retirement.