Remark 9.3.4.29. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category. For every object $X \in \operatorname{\mathcal{C}}$, the identity morphism $\operatorname{id}_{X}: X \rightarrow X$ is a monomorphism (Example 9.3.4.9), so we can regard $X$ as a subobject of itself. Moreover, the isomorphism class $[X]$ is a largest element of the partially ordered set $\operatorname{Sub}(X)$ (see Remark 9.3.2.21).
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