Abstract
In this paper quasi-bimonads on a monoidal category are introduced and investigated. Quasi-bimonads generalize quasi-bialgebras to a non-braided setting. We discuss their representations and investigate the R-matrix of a quasi-bimonad. Such an R-matrix provides a new solution of the version of the Yang-Baxter equation adapted to the situation. We also introduce an equivalent relation on (quasitriangular) quasi-bimonads such that the categories of representations of two (quasitriangular) quasi-bimonads are (braided) monoidal equivalent. Finally, we discuss Drinfeld twists and Hom quasi-bialgebras.
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