 Choose a natural isomorphism $\tau_{G}: G\Phi \xrightarrow{\sim} G$, for every $0$-morphism $G$ of ${\sc\mbox{G}\hspace{0.0pt}}_{L}$. The collection ${\left\{ \alpha_{G,F} \right\}}_{F,G \in {\sc\mbox{G}\hspace{0.0pt}}_{L}(\mathtt{i,i})}$