Notes on bimonads and Hopf monads
Mesablishvili, Bachuki ; Wisbauer, Robert
arXiv, 1010.3628 / Harvested from arXiv
For a generalisation of the classical theory of Hopf algebra over fields, A. Brugui\`eres and A. Virelizier study opmonoidal monads on monoidal categories (which they called {\em bimonads}). In a recent joint paper with S. Lack the same authors define the notion of a {\em pre-Hopf monad} by requiring only a special form of the fusion operator to be invertible. In previous papers it was observed by the present authors that bimonads yield a special case %Hopf monads may be considered as a special case of an entwining of a pair of functors (on arbitrary categories). The purpose of this note is to show that in this setting the pre-Hopf monads are a special case of Galois entwinings. As a byproduct some new properties are detected which make a (general) bimonad on a Cauchy complete category to a Hopf monad. In the final section applications to cartesian monoidal categories are considered.
Publié le : 2010-10-18
Classification:  Mathematics - Category Theory,  18A40, 16T15, 18C20
@article{1010.3628,
     author = {Mesablishvili, Bachuki and Wisbauer, Robert},
     title = {Notes on bimonads and Hopf monads},
     journal = {arXiv},
     volume = {2010},
     number = {0},
     year = {2010},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1010.3628}
}
Mesablishvili, Bachuki; Wisbauer, Robert. Notes on bimonads and Hopf monads. arXiv, Tome 2010 (2010) no. 0, . http://gdmltest.u-ga.fr/item/1010.3628/