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Is there a reference for the following?

Consider quasi-categories $I,C$. Suppose that a morphism between functors $\alpha : \Delta^1 \to Fun(I,C)$ is given. Suppose that for every $i \in I$, denoting the evaluation $ev_i : Fun(I,C) \to C$, the composition $ev_i \circ \alpha$ is an isomorphism (in the homotopy category). How to show then that $\alpha$ is an isomorphism (in the homotopy category)?

Thanks

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    $\begingroup$ Its in Rezk's notes "stuff about quasi categories" proposition 29.10 he also references HTT 3.1.1. there. $\endgroup$
    – Saal Hardali
    Commented Jan 26, 2019 at 7:37
  • $\begingroup$ @SaalHardali: Thank you! $\endgroup$
    – Sasha
    Commented Jan 26, 2019 at 7:41
  • $\begingroup$ You may also find that result as Theorem 5.14 in Joyal's The Theory of Quasi-Categories and its Applications. $\endgroup$
    – Daniel Gerigk
    Commented Jul 9, 2019 at 22:17

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Making my comment an answer to remove it from the unanswered list:

This is in Rezk's Stuff about quasicategories (pdf), Proposition 29.10.

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