Variant 4.9.7.6. 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 a small Kan complex: see Variant 4.9.5.6).
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$