A functor $F \colon \mathsf{C} \to \mathsf{D}$ is\n1. full if for each $x,y \in \mathsf{C}$, the map $\mathsf{C}(x,y) \to \mathsf{D}(Fx,Fy)$ is surjective;\n2. faithful if for each $x,y \in \mathsf{C}$, the map $\mathsf{C}(x,y) \to \mathsf{D}(Fx,Fy)$ is injective;\n3. and essentially surjective on objects if for every object $d \in \mathsf{D}$ there is some $c \in \mathsf{C}$ such that $d$ is isomorphic to $Fc$.