Hopf monads
By Alain Bruguières, Alexis Virelizier. 2006
123 citations recorded by the source corpus.
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).
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/3107cdd9de735e5f412a99631859c1cbf49d9971
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In Algebra and Number Theory
- G. Bòhm
- Kenichi Shimizu
- Stephen Lack
- Alexis Virelizier
- Alain Bruguières
- Tomasz Brzezinski
- Robert Wisbauer
- Michael Shulman
In Geometry and Topology
- G. Bòhm
- Kenichi Shimizu
- Stephen Lack
- Alexis Virelizier
- Alain Bruguières
- Robert Wisbauer
- Tomasz Brzezinski
- Michael Shulman
In Mathematical Physics
- G. Bòhm
- Kenichi Shimizu
- Stephen Lack
- Alexis Virelizier
- Alain Bruguières
- Robert Wisbauer
- Tomasz Brzezinski
- Michael Shulman
Citations in the corpus
- Hopf monads on monoidal categories (2010, methodology): “The notion of Hopf monad introduced in this paper is a generalization of the notion of Hopf monad on an autonomous category introduced in [5].”
- MONADS AND COMONADS ON MODULE CATEGORIES (2008, background): “aracterise Hopf algebras via their induced (co)monads. The following notions were introduced in [34] and [22]. Note that these terms have different meanings in Moerdijk [23] and Brugui`eres-Virelizier [6]. 8.9. Bimonads and Hopf monads. A bimonad on a category A is a functor F : A → A with a monad st”
- The monoidal center and the character algebra (2015, background): “onoidal functor. Since Fcommutes with the duality functor, we have F! ∼= F. Thus, for functors L,R: C → B, we have L⊣ F ⇐⇒ F⊣ L! and F⊣ R ⇐⇒ R! ⊣ F. Remark 2.4. Some of the above results are found in [BV07] and [BV12]. 3. Internal characters 3.1. The central Hopf monad. Throughout this section, we l”
- Hopf Algebroids (2008, methodology): “In the paper [15] special bimonads, so called Hopf monads, on autonomous categories were studied.”