I've got a question about levels of a topos, modalities and sheaves. Assume we have got a level for a topos $\mathcal{E}$, which induces adjoint (co)modalities $\Box\dashv\bigcirc$.
On the nLab page for Aufhebung (https://ncatlab.org/nlab/show/Aufhebung), it says that a sheaf for this level is an object $X$ which is isomorphic to $\bigcirc X$.
Now, this modality $\bigcirc:\mathcal{E}\to \mathcal{E}$ is a modality on the objects of the topos itself, rather than being a modality on its subobject classifier—for the latter, I understand the definition of a sheaf in the Lawvere-Tierney style.
Can someone help me relate the modality $\bigcirc$ with a Lawvere-Tierney operator, and more specifically, understand how the two notions of sheaf come to coincide?
Thanks!