Hey, if T is an ∞-topos and X is an object, is it true that X→lim_n τ_≤n X is an effective epi?
If that's too general, is it known to be true when X is a spectral Deligne-Mumford stack étale over Spet(R) for some ring R, and you view X as an object of the huge étale topos over R?