  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. These braidings are shown to arise from, and classify, cobraidings
(also known as coquasitriangular structures) on bialgebras. Using a
multicategorical approach we also describe examples of braidings on skew
monoidal categories arising from 2-category theory.
