Kerodon

$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$ $\newcommand\empty{}$
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$

Remark 5.5.3.11 (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 $\int ^{\mathrm{s}}_{\operatorname{\mathcal{C}}}\mathscr {F}$ 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 $\mathscr {F}(C)$.