Corollary 10.3.5.20. Let $\operatorname{\mathcal{C}}$ be a regular $\infty $-category and let $\operatorname{\mathcal{C}}_0 \subseteq \operatorname{\mathcal{C}}$ be a reflective subcategory, so that the inclusion functor $\operatorname{\mathcal{C}}_0 \hookrightarrow \operatorname{\mathcal{C}}$ admits a left adjoint $L: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{C}}_0$. If the functor $L$ preserves finite limits, then $\operatorname{\mathcal{C}}_0$ is a regular $\infty $-category and $L$ is a regular functor.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$