Remark 9.5.6.11. Let $\operatorname{\mathcal{C}}$ be a presentable $\infty $-category. If a full subcategory $\operatorname{\mathcal{C}}_0 \subseteq \operatorname{\mathcal{C}}$ is a Bousfield localization of $\operatorname{\mathcal{C}}$ (in the sense of Definition 9.5.6.9), then the inclusion $\operatorname{\mathcal{C}}_0 \hookrightarrow \operatorname{\mathcal{C}}$ admits a left adjoint $L: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{C}}_0$ which is a Bousfield localization functor (in the sense of Definition 9.5.6.1). Using Remark 6.3.3.12, we see that this construction determines a bijection
The inverse bijection carries a Bousfield localization functor $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ to the essential image its right adjoint.