If $\mathcal{C}$ is an essentially small category, is it true that $Ind(\mathcal{C})$, the full subcategory of $Fun(\mathcal{C},Set^{op})$ consisting of functors which can be expressed as filtered colimits of representable ones, is closed under small colimits?
I think that it should be equivalent to be closed under equalizers, since $Ind(\mathcal{C})$ is closed under filtered colimits, and hence under coproducts.
Thank you, Sasha