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



Reference request: levelwise detection of a morphism of $\infty$-functors being an isomorphism
Making my comment an answer to remove it from the unanswered list:


This is in Rezk's *Stuff about quasicategories* ([pdf](https://faculty.math.illinois.edu/~rezk/595-fal16/quasicats.pdf)), Proposition 29.10.


