# The monoidal Eilenberg-Moore construction and bialgebroids

Source: [The monoidal Eilenberg-Moore construction and bialgebroids](<https://www.sota2.com/research/paper/68fa4cb01e209131ce94e911>)

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

Data updated: 2025-10-25T08:54:17.388Z

Authors: K. Szlachanyi

Published: 2002-08-26T11:56:02.000Z

## Abstract

Monoidal functors U:C --\> M with left adjoints determine, in a universal way, monoids T in the category of oplax monoidal endofunctors on M. Such monads will be called bimonads. Treating bimonads as abstract "quantum groupoids" we derive Tannaka duality between left adjointable monoidal functors and bimonads. Bialgebroids, i.e., Takeuchi's x\_R-bialgebras, appear as the special case when T has also a right adjoint. Street's 2-category of monads then leads to a natural definition of the 2-category of bialgebroids.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/math/0208198>)

[PDF](<https://arxiv.org/pdf/math/0208198.pdf>)