Warning 4.1.2.5. The terminology of Definition 4.1.2.2 has the potential to cause confusion. If $\operatorname{\mathcal{C}}$ is an $\infty $-category and $\operatorname{\mathcal{C}}' \subseteq \operatorname{\mathcal{C}}$ is a subcategory, then $\operatorname{\mathcal{C}}'$ need not be (isomorphic to the nerve of) an ordinary category. Our use of the term “subcategory” (rather than the more technically correct “sub-$\infty $-category”) is intended to avoid awkward language.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$