A functor $F\colon \mathcal{C}\to \mathcal{D}$ is fully faithful if $F$ is full and faithful, i.e. if, 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 bijective.
