Remark 9.5.6.8. Let $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ be a Bousfield localization functor between presentable $\infty $-categories, and suppose we are given another functor $G: \operatorname{\mathcal{D}}\rightarrow \operatorname{\mathcal{E}}$. Then $G$ is cocontinuous if and only if $(G \circ F): \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{E}}$ is cocontinuous. This follows immediately from Remark 9.5.6.7.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$