= Solution
Take an <epimorphism> $\alpha:F\Rightarrow G$ in $[\mathcal C,\mathbf{Set}]$ and a <natural transformation> $\beta:\mathcal C(A,-)\Rightarrow G$. By the <Yoneda lemma>, $\beta$ corresponds to $x=\beta_A(1_A)\in G(A)$. By the <pointwise epimorphism in a functor category> criterion, choose $y\in F(A)$ with $\alpha_A(y)=x$.
The <Yoneda lemma> gives $\gamma_B(f)=F(f)(y)$, a <natural transformation> $\mathcal C(A,-)\Rightarrow F$. Naturality of $\alpha$ yields
$$
\alpha_B\gamma_B(f)=\alpha_BF(f)(y)=G(f)(\alpha_Ay)=G(f)(x)=\beta_B(f).
$$
Therefore \b[<covariant representables are projective>] in the set-valued <functor category>. Local smallness ensures that $\mathcal C(A,-)$ is set-valued.
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