# Kerodon

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Proposition 5.6.3.2. The simplicial set $\operatorname{\mathcal{S}}_{\ast }$ is an $\infty$-category, and the projection map $\operatorname{\mathcal{S}}_{\ast } \rightarrow \operatorname{\mathcal{S}}$ is a left fibration of $\infty$-categories.

Proof. By virtue of Proposition 5.6.1.2, the simplicial set $\operatorname{\mathcal{S}}$ is an $\infty$-category. It follows that for every object $X \in \operatorname{\mathcal{S}}$, the projection map $\operatorname{\mathcal{S}}_{X/} \rightarrow \operatorname{\mathcal{S}}$ is a left fibration (Corollary 4.3.6.11). Taking $X = \Delta ^{0}$, we conclude that the projection map $\operatorname{\mathcal{S}}_{\ast } \rightarrow \operatorname{\mathcal{S}}$ is a left fibration, so that $\operatorname{\mathcal{S}}_{\ast }$ is an $\infty$-category (Remark 4.2.1.4). $\square$