Remark 4.8.5.10 (Coproducts). Let $n$ be an integer, let $\{ F_ i: \operatorname{\mathcal{C}}_ i \rightarrow \operatorname{\mathcal{D}}_ i \} _{i \in I}$ be a collection of functors of $\infty $-categories, and let $F: \coprod _{i \in I} \operatorname{\mathcal{C}}_ i \rightarrow \coprod _{i \in I} \operatorname{\mathcal{D}}_ i$ be their coproduct. Then $F$ is categorically $n$-connective if and only if each $F_{i}$ is categorically $n$-connective. See Remark 4.8.2.11.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$