Example 10.2.2.13. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category containing a pair of morphisms $f_0, f_1: X \rightarrow Y$ which are homotopic. Then $f_0$ is a quotient morphism if and only if $f_1$ is a quotient morphism. This is a special case of Corollary 10.2.2.12, but can also be deduced immediately from the definition (since $f_0$ and $f_1$ generate the same sieve on $Y$).

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