An object $c$ in a category is called small, if there exists some regular cardinal $\kappa$ such that $Hom(c,-)$ preserves $\kappa$-filtered colimits.

Is there an example of a (locally small) category $C$ and an object $c$ of $C$, such that $c$ is not small, i.e. such that $Hom(c,-)$ doesn't preserve all $\kappa$-filtered colimits for any $\kappa$ whatsoever?