# Kerodon

$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$ $\newcommand\empty{}$

Proposition 4.4.3.6. Let $\operatorname{\mathcal{C}}$ be an $\infty$-category. Then the core $\operatorname{\mathcal{C}}^{\simeq }$ is a subcategory of $\operatorname{\mathcal{C}}$ (Definition 4.1.2.2): that is, the inclusion $\operatorname{\mathcal{C}}^{\simeq } \hookrightarrow \operatorname{\mathcal{C}}$ is an inner fibration.