# Kerodon

$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$ $\newcommand\empty{}$

Remark 3.3.2.7. The functor $X \mapsto \operatorname{Ex}(X)$ preserves filtered colimits of simplicial sets. To prove this, it suffices to observe that each of the simplicial sets $\operatorname{N}_{\bullet }( \operatorname{Chain}[n] )$ has only finitely many nondegenerate simplices (since the partially ordered set $\operatorname{Chain}[n])$ is finite).