# Kerodon

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

Proposition 1.1.4.1. The evaluation functor

$\operatorname{ev}_0: \operatorname{Set_{\Delta }}\rightarrow \operatorname{Set}\quad \quad X_{\bullet } \mapsto X_0$

restricts to an equivalence of categories

$\{ \textnormal{Simplicial sets of dimension \leq 0} \} \simeq \operatorname{Set}.$

Proof of Proposition 1.1.4.1. By virtue of Proposition 1.1.4.13, it will suffice to show that the construction $X_{\bullet } \mapsto X_0$ induces an equivalence of categories

$\{ \text{Discrete simplicial sets} \} \rightarrow \operatorname{Set}.$

This follows immediately from Corollary 1.1.4.10. $\square$