Corollary 7.3.8.14. Let $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ be a functor of $\infty $-categories which is left Kan extended from a full subcategory $\operatorname{\mathcal{C}}^{0} \subseteq \operatorname{\mathcal{C}}$. Then $F$ has a colimit in $\operatorname{\mathcal{D}}$ if and only if the restriction $F|_{\operatorname{\mathcal{C}}^{0}}$ has a colimit in $\operatorname{\mathcal{D}}$.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$
Proof. Apply Corollary 7.3.8.13 in the special case $\operatorname{\mathcal{E}}= \Delta ^0$. $\square$