Construction 4.4.3.1. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category. We let $\operatorname{\mathcal{C}}^{\simeq }$ denote the simplicial subset of $\operatorname{\mathcal{C}}$ comprised of those simplices $\sigma : \Delta ^{n} \rightarrow \operatorname{\mathcal{C}}$ which carry each edge of $\Delta ^ n$ to an isomorphism in $\operatorname{\mathcal{C}}$. We will refer to $\operatorname{\mathcal{C}}^{\simeq }$ as the core of $\operatorname{\mathcal{C}}$.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$