Remark 1.2.3.16. From the proof of Proposition 1.2.3.15, we can extract an explicit description of the realization $|S|^{Q}$: it can be realized as the colimit of the composite functor
\[ \operatorname{{\bf \Delta }}_{S} \rightarrow \operatorname{{\bf \Delta }}\xrightarrow {Q} \operatorname{\mathcal{C}}, \]
where $\operatorname{{\bf \Delta }}_{S}$ denotes the category of simplices of $S$ (Construction 1.1.3.9).