Remark 4.1.2.19. Let $\operatorname{\mathcal{C}}$ be an ordinary category. Then the construction $\operatorname{\mathcal{C}}' \mapsto \operatorname{N}_{\bullet }(\operatorname{\mathcal{C}}')$ induces a bijection
\[ \{ \textnormal{Full subcategories of $\operatorname{\mathcal{C}}$} \} \simeq \{ \textnormal{Full subcategories of $\operatorname{N}_{\bullet }(\operatorname{\mathcal{C}})$} \} . \]