Remark 9.3.2.20. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category and let $\operatorname{\mathcal{C}}' \subseteq \operatorname{\mathcal{C}}$ be the full subcategory spanned by the subterminal objects of $\operatorname{\mathcal{C}}$. Then the construction $X \mapsto [X]$ induces a trivial Kan fibration of $\infty $-categories $\operatorname{\mathcal{C}}' \rightarrow \operatorname{N}_{\bullet }( \operatorname{Sub}(\operatorname{\mathcal{C}}) )$. Stated more informally, the partially ordered set $\operatorname{Sub}(\operatorname{\mathcal{C}})$ can be identified with the full subcategory $\operatorname{\mathcal{C}}' \subseteq \operatorname{\mathcal{C}}$.
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