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Title: Weak bimonads and weak Hopf monads
Related: Journal of algebra, Vol. 328, Issue 1, (2011), p.1-30
DOI: 10.1016/j.jalgebra.2010.07.032
Publisher: Elsevier
Date: 2011
Author/Creator: Böhm, Gabriella
Author/Creator: Lack, Stephen
Author/Creator: Street, Ross
Description: We define a weak bimonad as a monad T on a monoidal category M with the property that the Eilenberg-Moore category MT is monoidal and the forgetful functor MT→M is separable Frobenius. Whenever M is also Cauchy complete, a simple set of axioms is provided, that characterizes the monoidal structure of MT 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.
Description: 30 page(s)
Subject Keyword: monads
Subject Keyword: monoidal categories
Subject Keyword: weak bimonads
Subject Keyword: weak Hopf monads
Subject Keyword: weak liftings
Resource Type: journal article
Organisation: Macquarie University. Dept. of Mathematics

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