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Hopf monads

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arxiv math/0604180 v2 pith:CXPTURXM submitted 2006-04-08 math.QA math.CT

Alain Bruguières , Alexis Virelizier This is my paper · ORCID
classification math.QAmath.CT
keywords hopfmonadscategoriesalgebrasautonomousintroducemonoidalnon-braided
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We introduce and study Hopf monads on autonomous categories (i.e., monoidal categories with duals). Hopf monads generalize Hopf algebras to a non-braided (and non-linear) setting. Indeed, any monoidal adjunction between autonomous categories gives rise to a Hopf monad. We extend many fundamental results of the theory of Hopf algebras (such as the decomposition of Hopf modules, the existence of integrals, Maschke's criterium of semisimplicity, etc...) to Hopf monads. We also introduce and study quasitriangular and ribbon Hopf monads (again defined in a non-braided setting).

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  1. Relative Invertibility and Full Dualizability of Finite Braided Tensor Categories

    math.QA 2025-06 accept novelty 8.0 of 10

    A finite braided tensor category is fully dualizable in the Morita 4-category of braided pre-tensor categories whenever its symmetric center is separable.

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