Bialgebra scalar cocycle
= Bialgebra scalar cocycle
{title2=$\gamma:H\otimes H\to k$}
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 $\gamma(1,a)=\varepsilon(a)=\gamma(a,1)$. Some conventions require convolution invertibility; that extra hypothesis distinguishes strong from lax tensor transformations.