• For each $A,B\in \text{Obj}\webleft (\mathcal{C}\webright )$, the restriction
    \[ F^{\textup{iso}}_{A,B} \colon \textup{Iso}_{\mathcal{C}}\webleft (A,B\webright ) \to \textup{Iso}_{\mathcal{D}}\webleft (F_{A},F_{B}\webright ) \]

    of the action on morphisms of $F$ at $\webleft (A,B\webright )$ to isomorphisms is surjective.


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