Corollary 1.2.3.5. The singular simplicial set functor $\operatorname{Sing}_{\bullet }: \operatorname{Top}\rightarrow \operatorname{Set_{\Delta }}$ admits a left adjoint, given by the geometric realization construction $S \mapsto | S|$.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$