Corollary 7.1.3.27. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category, let $\operatorname{\mathcal{C}}_0 \subseteq \operatorname{\mathcal{C}}$ be a reflective subcategory of $\operatorname{\mathcal{C}}$, and let $K$ be a simplicial set. If $\operatorname{\mathcal{C}}$ admits $K$-indexed limits, then $\operatorname{\mathcal{C}}_0$ also admits $K$-indexed limits. If $\operatorname{\mathcal{C}}$ admits $K$-indexed colimits, then $\operatorname{\mathcal{C}}_0$ also admits $K$-indexed colimits.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$