= Solution
Use <0-presentable object> in the specified sense: its hom-functor preserves all small <colimits>. For a <representable> $H_c$, the <Yoneda lemma> identifies this hom-functor with evaluation at $c$. Given any small diagram $P_j$, pointwise <colimits> give
$$
\begin{aligned}
\operatorname{Nat}\left(H_c,\operatorname{colim}_j P_j\right)
&\cong\left(\operatorname{colim}_jP_j\right)(c)\\
&=\operatorname{colim}_jP_j(c)\\
&\cong\operatorname{colim}_j\operatorname{Nat}(H_c,P_j).
\end{aligned}
$$
These are the canonical comparison <bijections>, including for an empty diagram. Therefore \b[every <representable presheaf> is 0-presentable], or a <small projective object> in this sense.
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