Variant 4.7.8.6. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category. We say that $\operatorname{\mathcal{C}}$ is locally small if, for every pair of objects $X,Y \in \operatorname{\mathcal{C}}$, the Kan complex $\operatorname{Hom}_{\operatorname{\mathcal{C}}}(X,Y)$ is essentially small (that is, it is homotopy equivalent to to a small Kan complex: see Variant 4.7.5.4).
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$