Kerodon

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

Example 4.6.1.3. Let $\operatorname{\mathcal{C}}$ be an ordinary category containing objects $X$ and $Y$, which we will identify with objects of the $\infty $-category $\operatorname{N}_{\bullet }(\operatorname{\mathcal{C}})$. Then the morphism space $\operatorname{Hom}_{ \operatorname{N}_{\bullet }(\operatorname{\mathcal{C}}) }( X, Y)$ of Construction 4.6.1.1 can be identified with the constant simplicial set having the value $\operatorname{Hom}_{\operatorname{\mathcal{C}}}(X,Y)$ (see Example 4.6.4.5).