Geodesic
Notes on Bimonads and Hopf Monads
Theory and applications of categories, Tome 26 (2012), pp. 281-303.

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

For a generalisation of the classical theory of Hopf algebra over fields, A. Bruguièeres and A. Virelizier study opmonoidal monads on monoidal categories (which they called bimonads,). In a recent joint paper with S. Lack the same authors define the notion of a 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 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 :
Classification : 18A40, 16T15, 18C20
Keywords: Opmonoidal functors, bimonads, Hopf monads, Galois entwinings 
@article{TAC_2012_26_a9,
     author = {Bachuki Mesablishvili and Robert Wisbauer},
     title = {Notes on {Bimonads} and {Hopf} {Monads}},
     journal = {Theory and applications of categories},
     pages = {281--303},
     publisher = {mathdoc},
     volume = {26},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2012_26_a9/}
}
TY  - JOUR
AU  - Bachuki Mesablishvili
AU  - Robert Wisbauer
TI  - Notes on Bimonads and Hopf Monads
JO  - Theory and applications of categories
PY  - 2012
SP  - 281
EP  - 303
VL  - 26
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TAC_2012_26_a9/
LA  - en
ID  - TAC_2012_26_a9
ER  - 
%0 Journal Article
%A Bachuki Mesablishvili
%A Robert Wisbauer
%T Notes on Bimonads and Hopf Monads
%J Theory and applications of categories
%D 2012
%P 281-303
%V 26
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TAC_2012_26_a9/
%G en
%F TAC_2012_26_a9
Bachuki Mesablishvili; Robert Wisbauer. Notes on Bimonads and Hopf Monads. Theory and applications of categories, Tome 26 (2012), pp. 281-303. http://geodesic.mathdoc.fr/item/TAC_2012_26_a9/