English

The monoidal Eilenberg-Moore construction and bialgebroids

Quantum Algebra 2007-05-23 v2 Category Theory

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.

Keywords

Cite

@article{arxiv.math/0208198,
  title  = {The monoidal Eilenberg-Moore construction and bialgebroids},
  author = {K. Szlachanyi},
  journal= {arXiv preprint arXiv:math/0208198},
  year   = {2007}
}

Comments

39 pages, AMSLaTeX