Kerodon

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

Example 7.2.3.11. Let $\mathscr {F}: \operatorname{\mathcal{C}}\rightarrow \operatorname{Set_{\Delta }}$ be a diagram of simplicial sets, and suppose that the category $\operatorname{\mathcal{C}}$ contains a final object $C$. Combining Lemma 7.2.3.10 with Corollary 4.6.6.25, we deduce that the inclusion map

\[ \mathscr {F}(C) \simeq \{ C\} \times _{ \operatorname{N}_{\bullet }(\operatorname{\mathcal{C}}) } \underset { \longrightarrow }{\mathrm{holim}}(\mathscr {F} ) \hookrightarrow \underset { \longrightarrow }{\mathrm{holim}}( \mathscr {F} ) \]

is right anodyne.