  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.
