Adjointable monoidal functors and quantum groupoids
Abstract
Every monoidal functor G: C --> M has a canonical factorization through the category of bimodules over some monoid R in M such that the factor U: C -->R MR is strongly unital. Using this result and the characterization of the forgetful functors MA -->R MR of bialgebroids A over R given by Schauenburg together with their bimonad description given by the author recently here we characterize the "long" forgetful functors MA -->R MR --> M of both bialgebroids and weak bialgebras.
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