# Kerodon

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Remark 1.1.2.3. For each $n \geq 0$, the standard $n$-simplex $\Delta ^ n$ is characterized by the following universal property: for every simplicial set $X_{\bullet }$, Yoneda's lemma supplies a bijection

$\operatorname{Hom}_{ \operatorname{Set_{\Delta }}}( \Delta ^ n, X_{\bullet } ) \simeq X_{n}.$

We will often invoke this bijection implicitly to identify $n$-simplices of $X_{\bullet }$ with maps of simplicial sets $\sigma : \Delta ^ n \rightarrow X_{\bullet }$.