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Article Dans Une Revue Advances in Mathematics Année : 2007

Hopf monads

Résumé

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).

Dates et versions

hal-00071050 , version 1 (22-05-2006)

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Alain Bruguières, Alexis Virelizier. Hopf monads. Advances in Mathematics, 2007, 215 (2), pp.679-733. ⟨10.1016/j.aim.2007.04.011⟩. ⟨hal-00071050⟩
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