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Feb 27, 2023 at 8:14 comment added Maxime Ramzi I don't think it is in general, but "inner fibration" is not a homotopical notion : any functor can be replaced, up to equivalence, by an inner fibration. I wrote this answer in terms of $\infty$-categories, not in terms of quasicategories.
Feb 27, 2023 at 4:44 comment added Lorenzo Riva Sorry, one more (probably obvious) thing - how do I show that $f$ is an inner fibration, which I need to apply 2.4.2.4?
Feb 23, 2023 at 10:50 comment added Maxime Ramzi @LorenzoRiva it depends what exactly you mean by "the very last argument", but yes, 2.4.2.4. was definitely implicit in a lot of what I wrote !
Feb 22, 2023 at 22:20 comment added Lorenzo Riva This is great, thanks! In the very last argument you are using (the dual to) HTT 2.4.2.4, right?
Feb 22, 2023 at 22:10 vote accept Lorenzo Riva
Feb 22, 2023 at 17:16 history answered Maxime Ramzi CC BY-SA 4.0