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Hopf monads

Authors
Journal
Advances in Mathematics
0001-8708
Publisher
Elsevier
Publication Date
Volume
215
Issue
2
Identifiers
DOI: 10.1016/j.aim.2007.04.011
Keywords
  • Hopf Monads
  • Monoidal Adjunctions
Disciplines
  • Mathematics

Abstract

Abstract 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. In particular, 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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