 Bialgebra scalar cocycle

A normalized scalar map $\gamma :H\otimes H\to k$ satisfying $\sum \gamma (a_{(1)},b_{(1)})\gamma (a_{(2)}{b}_{(2)},c)=\sum \gamma (b_{(1)},c_{(1)})\gamma (a,b_{(2)}{c}_{(2)})$, and $\gamma (1,a)=\epsilon (a)=\gamma (a,1)$. Some conventions require convolution invertibility; that extra hypothesis distinguishes strong from lax tensor transformations.