Kerodon

Example 6.3.3.10. 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 (Definition 6.2.2.19). Then $L$ is a reflective localization functor (since it is left adjoint to the inclusion map $\operatorname{\mathcal{C}}' \hookrightarrow \operatorname{\mathcal{C}}$; see Proposition 6.2.2.23). In particular, $L$ exhibits $\operatorname{\mathcal{C}}'$ as a localization of $\operatorname{\mathcal{C}}$ with respect to the collection of $\operatorname{\mathcal{C}}'$-local equivalences in $\operatorname{\mathcal{C}}$.