Faithful Functor

For categories \(C\) and \(D\), a functor \(F: C \to D\) is said to be faithful if, for every \(x, y \in C\), the map \(C(x, y) \to D(Fx, Fy)\) is injective.

Fully Faithful Functors

A faithful functor which is also a full functor is said to be a fully faithful functor.