Proposition 5.5.1.2. The simplicial set $\operatorname{\mathcal{S}}$ is an $\infty $-category.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$
Proposition 5.5.1.2. The simplicial set $\operatorname{\mathcal{S}}$ is an $\infty $-category.
Proof. By virtue of Theorem 2.4.5.1, it suffices to show that the simplicial category $\operatorname{Kan}$ is locally Kan: that is, for every pair of Kan complexes $X$ and $Y$, the simplicial set $\operatorname{Fun}(X,Y)$ is also a Kan complex. This is a special case of Corollary 3.1.3.4. $\square$