Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4666232 | Advances in Mathematics | 2012 | 37 Pages |
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 RR-modules are precisely the right bialgebroids over the ring RR. These skew-monoidal structures induce quotient skew-monoidal structures on the category of RR–RR-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.