Weak bimonads and weak Hopf monads
Category Theory
2014-05-21 v2 Quantum Algebra
Abstract
We define a weak bimonad as a monad T on a monoidal category M with the property that the Eilenberg-Moore category M^T is monoidal and the forgetful functor from M^T to M is separable Frobenius. Whenever M is also Cauchy complete, a simple set of axioms is provided, that characterizes the monoidal structure of M^T as a weak lifting of the monoidal structure of M . The relation to bimonads, and the relation to weak bimonoids in a braided monoidal category are revealed. We also discuss antipodes, obtaining the notion of weak Hopf monad.
Cite
@article{arxiv.1002.4493,
title = {Weak bimonads and weak Hopf monads},
author = {Gabriella Böhm and Stephen Lack and Ross Street},
journal= {arXiv preprint arXiv:1002.4493},
year = {2014}
}
Comments
29 pages; version 2 minor corrections and added references, also added remark 4.3; title changed from "Weak bimonads" to "Weak bimonads and weak Hopf monads"; to appear in Journal of Algebra