Exercise 8.4.1.11. Let $\operatorname{\mathcal{D}}$ denote the category of free abelian groups, and let $\operatorname{\mathcal{C}}\subseteq \operatorname{\mathcal{D}}$ denote the full subcategory spanned by object $\operatorname{\mathbf{Z}}$. Show that $\operatorname{\mathcal{C}}$ is not a dense subcategory of $\operatorname{\mathcal{D}}$. Consequently, the inclusion map $\operatorname{N}_{\bullet }(\operatorname{\mathcal{C}}) \subset \operatorname{N}_{\bullet }(\operatorname{\mathcal{D}})$ satisfies condition $(2)$ of Warning 8.4.1.10, but does not satisfy condition $(1)$.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$