• 2-Functoriality. The assignment $\mathcal{C}\mapsto \mathsf{Core}\webleft (\mathcal{C}\webright )$ defines a 2-functor
    \[ \mathsf{Core}\colon \mathsf{Cats}_{\mathsf{2}}\to \mathsf{Grpd}_{\mathsf{2}}. \]

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