# Adjointable monoidal functors and quantum groupoids

Source: [Adjointable monoidal functors and quantum groupoids](<https://www.sota2.com/research/paper/68fa4e571e209131ce95b4cd>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T09:46:52.240Z

Authors: K. Szlachanyi

Published: 2003-01-22T19:33:49.000Z

## 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.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/math/0301253>)

[PDF](<https://arxiv.org/pdf/math/0301253.pdf>)