Lawvere-Tierney topology [math-MRL4]

Let $\mathcal{E}$ be a topos. A Lawvere-Tierney topology in $\mathcal{E}$ is a morphism $j : \Omega \to \Omega$ such that the following diagrams are commutative:

A topology $j$ in a topos $\mathcal{E}$ gives rise to a new topos $\text{Sh}_j(E)$ defined over $\mathcal{E}$.