Remark 9.2.7.3. In the situation of Construction 9.2.7.1, the restriction map $\operatorname{Fun}( \Delta ^3, \operatorname{\mathcal{C}}) \rightarrow \operatorname{Fun}( Q, \operatorname{\mathcal{C}})$ is an isofibration of $\infty $-categories (Corollary 4.4.5.3). Moreover, since $Q$ contains every vertex of $\Delta ^3$, it is also conservative (Theorem 4.4.4.4). It follows that the solution space $\operatorname{Sol}(\sigma )$ is a Kan complex (Corollary 4.4.3.21).
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$