Definition 7.1.1.14. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category and let $K$ be a simplicial set. We will say that $\operatorname{\mathcal{C}}$ admits $K$-indexed limits if, for every diagram $u: K \rightarrow \operatorname{\mathcal{C}}$, there exists an object $Y \in \operatorname{\mathcal{C}}$ which is a limit of $u$. We will say that $\operatorname{\mathcal{C}}$ admits $K$-indexed colimits if, for every diagram $u: K \rightarrow \operatorname{\mathcal{C}}$, there exists an object $X \in \operatorname{\mathcal{C}}$ which is a colimit of $u$.
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