Corollary 9.6.9.25 (Classification of Bousfield Localizations). Let $\operatorname{\mathcal{C}}$ be a presentable $\infty $-category. Then there is a bijection
\[ \xymatrix@R =50pt@C=50pt{\{ \textnormal{Bousfield localizations $\operatorname{\mathcal{C}}_0 \subseteq \operatorname{\mathcal{C}}$} \} \ar [d]^{\sim }\\ \{ \textnormal{Accessibly strongly saturated collections of morphisms $\overline{W}$} \} } \]
which carries a Bousfield localization $\operatorname{\mathcal{C}}_0 \subseteq \operatorname{\mathcal{C}}$ to the collection of $\operatorname{\mathcal{C}}_0$-local equivalences in $\operatorname{\mathcal{C}}$.