Kerodon

$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$ $\newcommand\empty{}$
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$

Corollary 9.1.1.21. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category. Then the construction $W \mapsto \operatorname{\mathcal{C}}[W^{-1}]$ determines a bijection

\[ \xymatrix@R =50pt@C=50pt{ \{ \textnormal{Localizing collections of morphisms of $\operatorname{\mathcal{C}}$} \} \ar [d]^{\sim } \\ \{ \textnormal{Reflective replete subcategories of $\operatorname{\mathcal{C}}$} \} . } \]