The Braided Monoidal Structure on the Category of Comodules of Bimonads

Abstract

We investigate how the category of comodules of bimonads can be made into a monoidal category. It suffices that the monad and comonad in question are bimonads, with some extra compatibility relation. On a monoidal category of comodules of bimonads, we construct a braiding and get the necessary and sufficient conditions making it a braided monoidal category. As an application, we consider the category of comodules of corings and the category of entwined modules.