Variant 9.1.1.3. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category. We say that $\operatorname{\mathcal{C}}$ is cofiltered if, for every finite simplicial set $K$, every diagram $f: K \rightarrow \operatorname{\mathcal{C}}$ admits an extension $\overline{f}: K^{\triangleleft } \rightarrow \operatorname{\mathcal{C}}$. Equivalently, $\operatorname{\mathcal{C}}$ is cofiltered if the opposite $\infty $-category $\operatorname{\mathcal{C}}^{\operatorname{op}}$ is filtered.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$