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Adjointable monoidal functors and quantum groupoids

K. Szlachanyi
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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 M_R is strongly unital. Using this result and the characterization of the forgetful functors M_A -->_R M_R 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 M_A -->_R M_R --> M of both bialgebroids and weak bialgebras.

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K. Szlachanyi. 2003-01-22. Adjointable monoidal functors and quantum groupoids. https://arxiv.org/abs/math/0301253

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