The monoidal Eilenberg–Moore construction and bialgebroids

Strong monoidal functors U : C→ M with left adjoints determine, in a universal way, monoids T in the category of opmonoidal endofunctors on M . Treating such opmonoidal monads as abstract “quantum groupoids” we derive Tannaka duality between right adjoint strong monoidal functors and opmonoidal mona...

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Bibliographic Details
Published in:Journal of pure and applied algebra 2003-08, Vol.182 (2), p.287-315
Main Author: Szlachányi, Kornél
Format: Article
Language:English
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Summary:Strong monoidal functors U : C→ M with left adjoints determine, in a universal way, monoids T in the category of opmonoidal endofunctors on M . Treating such opmonoidal monads as abstract “quantum groupoids” we derive Tannaka duality between right adjoint strong monoidal functors and opmonoidal monads. Bialgebroids, i.e., Takeuchi's × 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.
ISSN:0022-4049
1873-1376
DOI:10.1016/S0022-4049(03)00018-5