Corollary 4.4.3.11. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category. Then the core $\operatorname{\mathcal{C}}^{\simeq }$ is a Kan complex.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$
Proof. Apply Proposition 4.4.3.7 to the isofibration $\operatorname{\mathcal{C}}\rightarrow \Delta ^{0}$. $\square$