Comodule natural transformation formula
= Comodule natural transformation formula
{title2=$\beta_M(u)=\sum u_{(0)}\alpha(u_{(1)})$}
A <natural transformation> between corestriction functors over a <field> has components $\beta_M(u)=\sum u_{(0)}\alpha(u_{(1)})$, recovered by $\alpha=\varepsilon\beta_H$. Monoidality forces $\alpha$ to be a unital <algebra homomorphism over a field>; for a <Hopf algebra>, $\alpha S$ supplies the inverse.