• For each $\mathcal{X}\in \text{Obj}\webleft (\mathsf{Cats}\webright )$ and each natural isomorphism
    of $\mathcal{C}$, there exists a natural isomorphism
    of $\mathcal{C}$ such that we have an equality
    of pasting diagrams in $\mathsf{Cats}_{\mathsf{2}}$, i.e. such that we have
    \[ \beta =\text{id}_{F}\mathbin {\star }\alpha . \]

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