Variant 4.7.9.2. Let $U: \operatorname{\mathcal{E}}\rightarrow \operatorname{\mathcal{C}}$ be an inner fibration of simplicial sets. We say that $U$ is essentially small if, for every simplex $\sigma : \Delta ^ n \rightarrow \operatorname{\mathcal{C}}$, the $\infty $-category $\Delta ^ n \times _{\operatorname{\mathcal{C}}} \operatorname{\mathcal{E}}$ is essentially small. We say that $U$ is locally small if, for every $n$-simplex $\sigma : \Delta ^ n \rightarrow \operatorname{\mathcal{C}}$, the $\infty $-category $\Delta ^ n \times _{\operatorname{\mathcal{C}}} \operatorname{\mathcal{E}}$ is locally small.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$