Full functor
= Full functor
A <functor> $F:\mathcal C\to\mathcal D$ is full when each function $\mathcal C(A,B)\to\mathcal D(FA,FB)$ is surjective. It is a <faithful functor> when each is injective. A <full and faithful functor> identifies its source, up to equivalence, with a <full subcategory> of the target. Fullness only concerns morphisms between image objects; it does not require every target object to lie in the image.