Notation 9.3.2.19. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category. We let $\operatorname{Sub}(\operatorname{\mathcal{C}})$ denote the collection of isomorphism classes of subterminal objects of $\operatorname{\mathcal{C}}$. If $X$ is a subterminal object of $\operatorname{\mathcal{C}}$, we let $[X] \in \operatorname{Sub}(\operatorname{\mathcal{C}})$ denote its isomorphism class. Given a pair of subterminal objects $X$ and $X'$, we write $[X] \subseteq [X']$ if there exists a morphism $f: X \rightarrow X'$ in the $\infty $-category $\operatorname{\mathcal{C}}$. Note that the relation $\subseteq $ is a partial ordering on the set $\operatorname{Sub}(\operatorname{\mathcal{C}})$.
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