# Kerodon

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

Remark 5.3.3.3 (Vertices of the Weighted Nerve). Let $\operatorname{\mathcal{C}}$ be a category equipped with a functor $\mathscr {F}: \operatorname{\mathcal{C}}\rightarrow \operatorname{Set_{\Delta }}$. Then vertices of the weighted nerve $\operatorname{N}_{\bullet }^{\mathscr {F}}(\operatorname{\mathcal{C}})$ can be identified with pairs $(C,x)$, where $C$ is an object of $\operatorname{\mathcal{C}}$ and $x$ is a vertex of the simplicial set $\mathscr {F}(C)$.