Projective cover of a set-valued functor by representables

For a small category $\mathcal{C}$ and $F:\mathcal{C}\to \mathbf{Set}$, the Yoneda lemma gives a canonical pointwise-surjective natural transformationEach representable is projective because evaluation preserves pointwise epimorphisms, and their coproduct is projective. Thus every set-valued functor on a small category is an epimorphic image of a projective object.