Skew-monoidal categories and bialgebroids

Details Skew-monoidal categories and bialgebroids Skew-monoidal categories and bialgebroids

2012-01-24

arxiv.org/abs/1201.4981v1

Mathematics

Quantum Algebra

34 pages

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Skew-monoidal categories and bialgebroids does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Skew-monoidal categories and bialgebroids, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Skew-monoidal categories and bialgebroids will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-107101