Example 4.6.1.16. In the situation of Construction 4.6.1.15, suppose that the simplicial $\operatorname{Hom}_{\operatorname{\mathcal{D}}}( q(X), q(Y) )$ is isomorphic to $\Delta ^0$ (this condition is satisfied, for example, if $\operatorname{\mathcal{D}}$ is the nerve of a partially ordered set). Then the inclusion map $\operatorname{Hom}_{\operatorname{\mathcal{C}}}(X,Y)_{e} \hookrightarrow \operatorname{Hom}_{\operatorname{\mathcal{C}}}(X,Y)$ is an isomorphism.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$