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Braided skew monoidal categories

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John Bourke and Stephen Lack

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.

Keywords:
Braiding, skew monoidal category, bialgebra,
quasitriangular, 2-category

2010 MSC:
18M50, 18M15, 18N10, 18N40, 16T10

*Theory and Applications of Categories,*
Vol. 35, 2020,
No. 2, pp 19-63.

Published 2020-01-21.

http://www.tac.mta.ca/tac/volumes/35/2/35-02.pdf

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