Corollary 4.5.6.13. Let $\operatorname{\mathcal{C}}$ be a small category and let $\mathscr {F}: \operatorname{\mathcal{C}}\rightarrow \operatorname{Set_{\Delta }}$ be an isofibrant diagram of simplicial sets. Then the limit $\varprojlim ( \mathscr {F} )$ is an $\infty $-category.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$
Proof. Apply Corollary 4.5.6.12 in the special case $\mathscr {E} = \underline{ \Delta ^{0} }$. $\square$