Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Weak bimonads and weak Hopf monads   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.

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The categories of this paper are: math-ph
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The categories of this paper are: adap-org
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The categories of this paper are: q-alg
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The categories of this paper are: comp-gas
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The categories of this paper are: dg-ga
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The categories of this paper are: cond-mat
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The categories of this paper are: quant-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-th
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The categories of this paper are: solv-int
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: bayes-an
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The categories of this paper are: q-bio
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The categories of this paper are: funct-an
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The categories of this paper are: hep-ex