Publication details

Braided skew monoidal categories

Authors

BOURKE John Denis LACK Stephen

Year of publication 2020
Type Article in Periodical
Magazine / Source Theory and Applications of Categories
MU Faculty or unit

Faculty of Science

Citation
Web http://www.tac.mta.ca/tac/volumes/35/2/35-02.pdf
Keywords Braiding; skew monoidal category; bialgebra; quasitriangular; 2-category
Description We introduce the notion of a braiding on a skew monoidal category, whose curious feature is that the defining isomorphisms involve three objects rather than two. Examples are shown to arise from 2-category theory and from bialgebras. In order to describe the 2-categorical examples, we take a multicategorical approach. We explain how certain braided skew monoidal structures in the 2-categorical setting give rise to braided monoidal bicategories. For the bialgebraic examples, we show that, for a skew monoidal category arising from a bialgebra, braidings on the skew monoidal category are in bijection with cobraidings (also known as coquasitriangular structures) on the bialgebra.

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