Coquasitriangular Hopf group coalgebras and braided monoidal categories.

Let π be a group, and let H be a Hopf π-coalgebra. We first show that the category M of right π-comodules over H is a monoidal category and there is a monoidal endofunctor ( F, id, id) of M for any α ∈ π. Then we give the definition of coquasitriangular Hopf π-coalgebras. Finally, we show that H is a coquasitriangular Hopf π-coalgebra if and only if M is a braided monoidal category and ( F, id, id) is a braided monoidal endofunctor of M for any α ∈ π. [ABSTRACT FROM AUTHOR]