Given categories $\mathsf{C},\mathsf{D}$ with a functor $F:\mathsf{C}\to\mathsf{D}$, the functor $F$ is
full if the map $\text{Hom}(x,y)\to\text{Hom}(Fx,Fy)$ is surjective
faithful if the map $\text{Hom}(x,y)\to\text{Hom}(Fx,Fy)$ is injective
essentially surjective on objects if for every object $d\in\mathsf{D}$ there is an object $c\in\mathsf{C}$ such that $d$ is isomorphic to $Fc$