Remark 2.2.8.6. The terminology of Definition 2.2.8.5 fits into a general paradigm. Given $0 \leq m \leq n \leq \infty $, let us informally use the term $(n,m)$-category to refer to an $n$-category $\operatorname{\mathcal{C}}$ having the property that every $k$-morphism of $\operatorname{\mathcal{C}}$ is invertible for $k > m$. Following this convention, the $\infty $-categories of Definition 1.4.0.1 should really be called $(\infty ,1)$-categories.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$