Kerodon

Remark 6.3.3.8. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category. Up to equivalence, every reflective localization functor $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ can be obtained from the construction of Example 6.3.3.7. More precisely, if $G$ is a fully faithful right adjoint to $F$, then it induces an equivalence of $\operatorname{\mathcal{D}}$ with a reflective subcategory $\operatorname{\mathcal{C}}' \subseteq \operatorname{\mathcal{C}}$ (carrying $F$ to the $\operatorname{\mathcal{C}}'$-reflection functor $(G \circ F): \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{C}}'$); see Corollary 6.2.2.19.