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 \alpha \in \pi. 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 \alpha \in \pi.

Keywords

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

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