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Timeline for Pullback of localizations

Current License: CC BY-SA 4.0

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Sep 24 at 23:39 vote accept user39598
S Sep 24 at 23:39 history bounty ended user39598
S Sep 24 at 23:39 history notice removed user39598
Sep 23 at 17:31 answer added Maxime Ramzi timeline score: 4
S Sep 23 at 12:18 history bounty started user39598
S Sep 23 at 12:18 history notice added user39598 Canonical answer required
S Aug 24 at 3:05 history bounty ended CommunityBot
S Aug 24 at 3:05 history notice removed CommunityBot
S Aug 16 at 1:28 history bounty started user39598
S Aug 16 at 1:28 history notice added user39598 Canonical answer required
Jul 25 at 19:26 comment added user39598 I believe that if $F$ is a reflective localization (with right adjoint $i$) and coCartesian fibration, then $F$ is universally localizing. This is because the fiber $E_b$ of $F: E \rightarrow B$ over $b$ is the full subcategory of overcategory $E_{ / i(b)}$ whose objects are $f: e \rightarrow i(b)$ so that $F(f)$ is an isomorphism. This has a terminal object $Id_{i(b)}: i(b) \rightarrow i(b)$ and so the fiber is weakly contractible.
Jul 25 at 13:38 history asked user39598 CC BY-SA 4.0