Traced premonoidal categories

Nick Benton; Martin Hyland

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Quasitriangular Hopf group algebras and braided monoidal categories

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Let $π$ be a group, and $H$ be a semi-Hopf $π$ -algebra. We first show that the category $_{H} ℳ$ of left $π$ -modules over $H$ is a monoidal category with a suitably defined tensor product and each element $α$ in $π$ induces a strict monoidal functor $F_{α}$ from $_{H} ℳ$ to itself. Then we introduce the concept of quasitriangular semi-Hopf $π$ -algebra, and show that a semi-Hopf $π$ -algebra $H$ is quasitriangular if and only if the category $_{H} ℳ$ is a braided monoidal category and $F_{α}$ is a strict braided monoidal functor for any...