nLab
ff morphism

A morphism $f:A\to B$ in a 2-category $K$ is called ff or fully-faithful if for all objects $X$, the functor

$$K(X,A)\to K(X,B)$$K(X,A) \to K(X,B)

is full and faithful. One easily checks that in Cat this is the same as $f$ itself being full and faithful.