Notes on bimonads and Hopf monads

Details Notes on bimonads and Hopf monads Notes on bimonads and Hopf monads

2010-10-18

arxiv.org/abs/1010.3628v2

Mathematics

Category Theory

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Notes on bimonads and Hopf monads does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Notes on bimonads and Hopf monads, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Notes on bimonads and Hopf monads will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-306289