Given a topos $\mathcal{E}$ with subobject classifier $\Omega$.

If we denote by $N\Omega$ the former of all local operators on $\Omega$, that is, Lawvere–Tierney topologies of $\mathcal{E}$, it is know that $N\Omega$ forms a Heyting algebra. Also $\Omega$ is a internal Heyting algebra in $\mathcal{E}$.

There exists a morphism from $\Omega$ to $N\Omega$?