Multiplication compatibility for a comodule tensor transformation ($m\ast \gamma =\gamma \ast n$)

For a transformation from the tensor built using $n$ to the tensor built using $m$, colinearity is $m\ast \gamma =\gamma \ast n$: $\sum m(a_{(1)},b_{(1)})\gamma (a_{(2)},b_{(2)})=\sum \gamma (a_{(1)},b_{(1)})n(a_{(2)},b_{(2)})$. Scalar maps enter this convolution product for coalgebra maps via the common algebra unit.