Kerodon

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

Example 5.5.3.6 (The Weighted Nerve of a Constant Diagram). Let $\operatorname{\mathcal{C}}$ be a category, let $X$ be a simplicial set, and let $\mathscr {F}: \operatorname{\mathcal{C}}\rightarrow \operatorname{Set_{\Delta }}$ be the constant functor taking the value $X$. Then Remark 5.5.3.5 and Example 5.5.3.2 supply an isomorphism of simplicial sets $\int ^{\mathrm{s}}_{\operatorname{\mathcal{C}}}\mathscr {F} \simeq X \times \operatorname{N}_{\bullet }(\operatorname{\mathcal{C}})$.