Corollary 9.6.9.14 (Classification of Accessible Factorization Systems). Let $\operatorname{\mathcal{C}}$ be a presentable $\infty $-category. Then the construction $(S_ L, S_ R) \mapsto S_{L}$ induces a bijection
\[ \xymatrix@R =50pt@C=50pt{ \{ \textnormal{Accessible factorization systems $(S_ L,S_ R)$ on $\operatorname{\mathcal{C}}$} \} \ar [d]^{\sim } \\ \{ \textnormal{Accessibly saturated collections of morphisms $\overline{W}$ of $\operatorname{\mathcal{C}}$} \} . } \]