Remark 8.1.1.4. The construction $\operatorname{\mathcal{C}}\mapsto \operatorname{Tw}(\operatorname{\mathcal{C}})$ determines a functor from the category of simplicial sets to itself, which preserves all limits and colimits (this follows from Remark 8.1.1.2, since limits and colimits in the category $\operatorname{Set_{\Delta }}$ are computed levelwise).

$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$