Remark 1.1.3.13. It follows from the proof of Proposition 1.1.3.11 that every simplicial set $S$ can be recovered as the colimit $\varinjlim _{ ( [n], \sigma ) \in \operatorname{{\bf \Delta }}_{S} } \Delta ^ n$. In fact, this is a general feature of presheaf categories: see Theorem 8.4.2.1 for an $\infty $-categorical counterpart.
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