• The functor $F$ is faithful, i.e. for each $A,B\in \text{Obj}\webleft (\mathcal{C}\webright )$, the action on morphisms
    \[ F_{A,B} \colon \textup{Hom}_{\mathcal{C}}\webleft (A,B\webright ) \to \textup{Hom}_{\mathcal{D}}\webleft (F_{A},F_{B}\webright ) \]

    of $F$ at $\webleft (A,B\webright )$ is injective.


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