Remark 6.2.2.21. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category, let $\operatorname{\mathcal{C}}' \subseteq \operatorname{\mathcal{C}}$ be a reflective subcategory, and let $L: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{C}}$ be a $\operatorname{\mathcal{C}}'$-reflection functor. Then a morphism $f: X \rightarrow Y$ of $\operatorname{\mathcal{C}}$ is a $\operatorname{\mathcal{C}}'$-local equivalence (in the sense of Definition 6.2.2.1) if and only if $L(f)$ is an isomorphism in the $\infty $-category $\operatorname{\mathcal{C}}'$.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$