nLab
locally fully faithful 2-functor

Definition

A 2-functor $F:C\to D$ is locally fully faithful if each functor on hom-categories

$$F:C(x,y)\to D(Fx,Fy)$$F \colon C(x,y) \to D(F x, F y)

is fully faithful.

Related pages

• full and faithful 2-functor

• 2-category equipped with proarrows