Remark 4.5.1.17. Let $\{ F_ i: \operatorname{\mathcal{C}}_ i \rightarrow \operatorname{\mathcal{D}}_{i} \} _{i \in I}$ be a collection of functors between $\infty $-categories indexed by a set $I$. If each $F_{i}$ is an equivalence of $\infty $-categories, then the product functor $\prod _{i \in I} \operatorname{\mathcal{C}}_{i} \rightarrow \prod _{i \in I} \operatorname{\mathcal{D}}_ i$ is also an equivalence of $\infty $-categories.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$