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Coquasitriangular Hopf group coalgebras and braided monoidal categories. (English) Zbl 1229.16024

Summary: Let \(\pi\) be a group, and let \(H\) be a Hopf \(\pi\)-coalgebra. We first show that the category \(\mathcal M^H\) of right \(\pi\)-comodules over \(H\) is a monoidal category and there is a monoidal endofunctor \((F_\alpha,\text{id},\text{id})\) of \(\mathcal M^H\) for any \(\alpha\in\pi\). Then we give the definition of coquasitriangular Hopf \(\pi\)-coalgebras. Finally, we show that \(H\) is a coquasitriangular Hopf \(\pi\)-coalgebra if and only if \(\mathcal M^H\) is a braided monoidal category and \((F_\alpha,\text{id},\text{id})\) is a braided monoidal endofunctor of \(\mathcal M^H\) for any \(\alpha\in\pi\).

MSC:

16T15 Coalgebras and comodules; corings
18D10 Monoidal, symmetric monoidal and braided categories (MSC2010)
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References:

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