Bimonads and Hopf monads on categories

@article{Mesablishvili2007BimonadsAH,
  title={Bimonads and Hopf monads on categories},
  author={Bachuki Mesablishvili and Robert Wisbauer},
  journal={Journal of K-theory},
  year={2007},
  volume={7},
  pages={349-388}
}
The purpose of this paper is to develop a theory of bimonads and Hopf monads on arbitrary categories thus providing the possibility to transfer the essentials of the theory of Hopf algebras in vector spaces to more general settings. There are several extensions of this theory to monoidal categories which in a certain sense follow the classical trace. Here we do not pose any conditions on our base category but we do refer to the monoidal structure of the category of endofunctors on any category… 
ON BIMONADS AND HOPF MONADS
For a generalisation of the classical theory of Hopf algebra over fields, A. Bruguières and A. Virelizier study opmonoidal monads on monoidal categories (which they called bimonads). In a recent
NOTES ON BIMONADS AND HOPF MONADS
For a generalisation of the classical theory of Hopf algebra over fields, A. Bruguieres and A. Virelizier study opmonoidal monads on monoidal categories (which they called bimonads). In a recent
GENERALIZED HOPF MODULES FOR BIMONADS
Brugui eres, Lack and Virelizier have recently obtained a vast generaliza- tion of Sweedler's Fundamental Theorem of Hopf modules, in which the role of the Hopf algebra is played by a bimonad. We
CYCLIC HOMOLOGY ARISING FROM ADJUNCTIONS
Given a monad and a comonad, one obtains a distributive law between them from lifts of one through an adjunction for the other. In particular, this yields for any bialgebroid the Yetter-Drinfel'd
Galois functors and generalised Hopf modules
As shown in a previous paper by the same authors, the theory of Galois functors provides a categorical framework for the characterisation of bimonads on any category as Hopf monads and also for the
Monads on Higher Monoidal Categories
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The structure and conditions that guarantee that the higher monoidal structure is inherited by the category of algebras over the monad are identified.
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In this paper, we introduce and investigate semicorings over associative semirings and their categories of semicomodules. Our results generalize old and recent ones on corings over rings and their
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In category theory, monads, which are monoid objects on endofunctors, play a central role closely related to adjunctions. Monads have been studied mostly in algebraic situations. In this
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