$L^{\prime }$-localization in an $\infty$-topos

Abstract

We prove that, given any reflective subfibration $L_{\bullet }$ on an $\infty$-topos $\mathcal{E}$, there exists a reflective subfibration $L_{\bullet }^{\prime }$ 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".

26 pages

References in corpus (2)

• Higher Topos Theory
• Modalities in homotopy type theory

Cited by in corpus (1)

• Detecting isomorphisms in the homotopy category