• Associativity. Let

    be a diagram in $\mathsf{Cats}_{\mathsf{2}}$. The diagram

    commutes, i.e. given natural transformations

    we have

    \[ \webleft (\gamma \mathbin {\star }\beta \webright )\mathbin {\star }\alpha =\gamma \mathbin {\star }\webleft (\beta \mathbin {\star }\alpha \webright ). \]

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