  We prove that, given any reflective subfibration $L_\bullet$ on an
$\infty$-topos $\mathcal{E}$, there exists a reflective subfibration
$L'_\bullet$ on $\mathcal{E}$ whose local maps are the $L$-separated maps, that
is, the maps whose diagonals are $L$-local. This is the companion paper to
"Localization theory in an $\infty$-topos".
