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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, thatis, the maps whose diagonals are $L$-local. This is the companion paper to"Localization theory in an $\infty$-topos".

$L'$-localization in an $\infty$-topos