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

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