Kerodon

Remark 9.5.6.14. Let $\operatorname{\mathcal{C}}$ be a presentable $\infty $-category and let $\operatorname{\mathcal{C}}_0$ be a replete full subcategory. Then $\operatorname{\mathcal{C}}_0$ is a Bousfield localization of $\operatorname{\mathcal{C}}$ if and only if the inclusion functor $\operatorname{\mathcal{C}}_0 \hookrightarrow \operatorname{\mathcal{C}}$ admits a left adjoint $L: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{C}}_0$ which is accessible when viewed as a functor from $\operatorname{\mathcal{C}}$ to itself. See Proposition 9.4.7.9.