Comodule tensor transformation formula
= Comodule tensor transformation formula
{title2=$\varphi(u\otimes v)=\sum u_{(0)}\otimes v_{(0)}\gamma(u_{(1)},v_{(1)})$}
A natural underlying transformation of tensor bifunctors on right <comodules> over a <field> has components $\varphi_{M,N}(u\otimes v)=\sum u_{(0)}\otimes v_{(0)}\gamma(u_{(1)},v_{(1)})$. Recover $\gamma=(\varepsilon\otimes\varepsilon)\varphi_{H,H}$; colinearity and monoidal axioms impose further equations.