Remark 3.4.6.5. In the situation of Definition 3.4.6.4, the simplicial set $\operatorname{Sing}_{\bullet }^{\operatorname{\mathcal{U}}}(X)$ is given by the union $\bigcup _{U \in \operatorname{\mathcal{U}}} \operatorname{Sing}_{\bullet }(U)$, where we regard each $\operatorname{Sing}_{\bullet }(U)$ as a simplicial subset of $\operatorname{Sing}_{\bullet }(X)$.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$