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Sep 20, 2023 at 16:36 answer added Simon Henry timeline score: 4
Sep 19, 2023 at 18:11 comment added Tim Campion @SimonHenry Er.... I suppose so.
Sep 19, 2023 at 16:49 comment added Simon Henry Doesn't a possitive answer to your question imply that the identity of $Cat_\infty$ can be factor through a 1-category (the essentialy image of $\Phi$) ? because this is clearly impossible! Unless "coproduct" is interpreted as "$\infty$-groupoid indexed colimits", in whcih case the construction you do in the begining applied to a Segal space instead of a quasicategory should do the trick.
Sep 19, 2023 at 16:33 history asked Tim Campion CC BY-SA 4.0