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Jul 30, 2023 at 20:38 comment added Peter LeFanu Lumsdaine @TimCampion: Fantastic, thanks — edited into the answer.
Jul 30, 2023 at 20:37 history edited Peter LeFanu Lumsdaine CC BY-SA 4.0
added precise reference in Cisinki (thanks Tim C) and added more details on the analogous results for the Voevodsky universe
Jul 30, 2023 at 18:10 comment added Tim Campion It appears in the proof of Thm 1.4.3. Note that Cisinski calls the subobject classifier "the Lawvere object". See also 1.3.9
Jul 30, 2023 at 15:21 history edited Peter LeFanu Lumsdaine CC BY-SA 4.0
fixed obvious blooper (thanks Zhen Lin!) and added note on references
Jul 30, 2023 at 15:02 comment added Peter LeFanu Lumsdaine @ZhenLin: D’oh, of course — thanks!
Jul 30, 2023 at 12:16 comment added Arshak Aivazian Wow, indeed, thanks!
Jul 30, 2023 at 12:15 vote accept Arshak Aivazian
Jul 30, 2023 at 6:20 comment added Zhen Lin Presumably you mean trivially fibrant.
Jul 29, 2023 at 23:25 history answered Peter LeFanu Lumsdaine CC BY-SA 4.0