Definition 7.6.6.20. Let $\mathbb {K}$ be a collection of simplicial sets. We say that an $\infty $-category $\operatorname{\mathcal{C}}$ is $\mathbb {K}$-complete if it admits $K$-indexed limits, for each $K \in \mathbb {K}$. We say that $\operatorname{\mathcal{C}}$ is $\mathbb {K}$-cocomplete if it admits $K$-indexed colimits, for each $K \in \mathbb {K}$.
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