If $F$ is a contravariant functor from $Sets$ to $Sets$. And for any functor $H: I \to Sets$ that has a colimit $C$ we have $F(C)$ is a limit for $F \circ H: I ^{op} \to Sets $. Show that $F$ is representable.
I have no idea how to start. I think I should take some $I$ and $H$ and using the colimit of it as a represent. But I have no idea how to find such $I$ or $H$. Any help is appreciated.