Remark 3.3.2.6. The construction $X \mapsto \operatorname{Ex}(X)$ can be regarded as a special case of Variant 1.2.2.8: it is the functor $\operatorname{Sing}_{\bullet }^{T}: \operatorname{Set_{\Delta }}\rightarrow \operatorname{Set_{\Delta }}$ associated to the cosimplicial object $T$ of $\operatorname{Set_{\Delta }}$ given by the construction $[n] \mapsto \operatorname{N}_{\bullet }( \operatorname{Chain}[n] )$.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$