Example 4.5.1.11. Let $\operatorname{\mathcal{C}}$ and $\operatorname{\mathcal{D}}$ be $\infty $-categories, and let $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ be an isomorphism of simplicial sets. Then $F$ is an equivalence of $\infty $-categories. In particular, for every $\infty $-category $\operatorname{\mathcal{C}}$, the identity functor $\operatorname{id}_{\operatorname{\mathcal{C}}}$ is an equivalence of $\infty $-categories.
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