presheaves topoi - is it enough to prove that a functor preserves small colimits to get a left adjoint?

Question

I have a certain functor $F:\mathbf{Set}^{\mathcal{O}(X)^{\mathsf{op}}}\rightarrow \mathbf{Set}^{\mathcal{O}(Y)^{\mathsf{op}}}$, where $X,Y$ are topological spaces, and I want to prove that it is the inverse image of a geometric morphism. So I need to prove that $F$ has a right adjoint and that it preserves finite limits.
In this discussion Show that a functor which preserves colimits has a right adjoint it is proved that if a functor between presheaves topoi preserves colimits then it has a right adjoint.
My question is: in my proof should I care only about preservation of small colimits?