Remark 7.1.3.8. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category and let $f: K \rightarrow \operatorname{\mathcal{C}}$ be a morphism of simplicial sets. An extension $\overline{f}: K^{\triangleright } \rightarrow \operatorname{\mathcal{C}}$ is a colimit diagram in $\operatorname{\mathcal{C}}$ if and only if the opposite map $\overline{f}^{\operatorname{op}}: (K^{\operatorname{op}})^{\triangleleft } \rightarrow \operatorname{\mathcal{C}}^{\operatorname{op}}$ is a limit diagram in the $\infty $-category $\operatorname{\mathcal{C}}^{\operatorname{op}}$.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$