Variant 9.1.10.3. Let $\mathscr {F}: \operatorname{\mathcal{J}}\rightarrow \operatorname{\mathcal{S}}$ be a filtered diagram of spaces. Assume that, for every object $C \in \operatorname{\mathcal{C}}$, the Kan complex $\mathscr {F}(C)$ is $n$-truncated for some fixed integer $n$. Then the colimit $\varinjlim (\mathscr {F})$ is also $n$-truncated.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$