Definition 9.3.2.1. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category. We will say that an object $X \in \operatorname{\mathcal{C}}$ is discrete if, for every object $C \in \operatorname{\mathcal{C}}$, every connected component of the morphism space $\operatorname{Hom}_{\operatorname{\mathcal{C}}}(C,X)$ is contractible.
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