  Skew-monoidal categories arise when the associator and the left and right
units of a monoidal category are, in a specific way, not invertible. We prove
that the closed skew-monoidal structures on the category of right R-modules are
precisely the right bialgebroids over the ring R. These skew-monoidal
structures induce quotient skew-monoidal structures on the category of
R-R-bimodules and this leads to the following generalization: Opmonoidal monads
on a monoidal category correspond to skew-monoidal structures with the same
unit object which are compatible with the ordinary monoidal structure by means
of a natural distributive law. Pursuing a Theorem of Day and Street we also
discuss monoidal lax comonads to describe the comodule categories of
bialgebroids beyond the flat case.
