The monoidal Eilenberg-Moore construction and bialgebroids (Q1399150)

Strong monoidal functors \(U:{\mathcal C}\to{\mathcal M}\) with left adjoint determine, in a universal way, monoids \(T\) in the category of opmonoidal endofunctors on \({\mathcal M}\). Using this the author derives Tannaka duality between right adjoint strong monoidal functors and opmonoidal monads. Bialgebroids appear as a special case when \(T\) admits a right adjoint. Street's 2-category of monads then leads to a natural definition of 2-category of bialgebroids.