Example 7.1.4.7. Let $\{ \operatorname{\mathcal{C}}_{i} \} _{i \in I}$ be a collection of $\infty $-categories having a product $\operatorname{\mathcal{C}}= \prod _{i \in I} \operatorname{\mathcal{C}}_ i$. Then the projection functors $\operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{C}}_ i$ preserve $K$-indexed limits and colimits, for every simplicial set $K$. See Example 7.1.3.11.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$