The monoidal Eilenberg-Moore construction and bialgebroids

Details The monoidal Eilenberg-Moore construction and bialgebroids The monoidal Eilenberg-Moore construction and bialgebroids

2002-08-26

arxiv.org/abs/math/0208198v2

Mathematics

Quantum Algebra

39 pages, AMSLaTeX

Scientific paper

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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