Kerodon

$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$

Corollary 4.4.3.9. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category. Then the core $\operatorname{\mathcal{C}}^{\simeq }$ is a Kan complex.

Proof. Apply Proposition 4.4.3.6 to the isofibration $\operatorname{\mathcal{C}}\rightarrow \Delta ^{0}$. $\square$