Coquasitriangular Hopf group coalgebras and braided monoidal categories

Abstract

Let π be a group, and let H be a Hopf π-coalgebra. We first show that the category M ^H of right π-comodules over H is a monoidal category and there is a monoidal endofunctor (F _α, id, id) of M ^H 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 ^H is a braided monoidal category and (F _α, id, id) is a braided monoidal endofunctor of M ^H for any α ∈ π.

Keywords

H-π-comodule / braided monoidal category / braided monoidal functor

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