= Cobraided bialgebra
{title2=$(H,r)$}
= Coquasitriangular bialgebra
{synonym}
A <bialgebra> equipped with a <coquasitriangular structure>, namely a convolution-invertible scalar form $r:H\otimes H\to k$ satisfying $r(ab,c)=\sum r(a,c_{(1)})r(b,c_{(2)})$, $r(a,bc)=\sum r(a_{(1)},c)r(a_{(2)},b)$ and $\sum r(a_{(1)},b_{(1)})a_{(2)}b_{(2)}=\sum b_{(1)}a_{(1)}r(a_{(2)},b_{(2)})$, with unit normalization. The induced right-<comodule> <braiding> is $v\otimes w\mapsto\sum w_{(0)}\otimes v_{(0)}r(v_{(1)},w_{(1)})$.
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