# Kerodon

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Example 5.5.3.7 (Fibers of the Weighted Nerve). Let $\mathscr {F}: \operatorname{\mathcal{C}}\rightarrow \operatorname{Set_{\Delta }}$ be functor. For each object $C \in \operatorname{\mathcal{C}}$, Remark 5.5.3.5 and Example 5.5.3.2 supply an isomorphism of simplicial sets

$\mathscr {F}(C) \simeq \{ C\} \times _{ \operatorname{N}_{\bullet }( \operatorname{\mathcal{C}}) } \int ^{\mathrm{s}}_{\operatorname{\mathcal{C}}}\mathscr {F}.$