Warning 9.5.7.7. The converse of Corollary 9.5.7.6 is false in general. For example, if $X$ is an acyclic Kan complex which is not contractible, then the colimit functor $\varinjlim : \operatorname{Fun}(X, \operatorname{\mathcal{S}}) \rightarrow \operatorname{\mathcal{S}}$ is an epimorphism in the $\infty $-category $\operatorname{\mathcal{QC}}^{\operatorname{LPr}}$ which is not a Bousfield localization functor (compare with Remark 6.3.3.2).
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$