Definition 7.6.6.1. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category. We say that $\operatorname{\mathcal{C}}$ is complete if it admits $K$-indexed limits, for every small simplicial set $K$. We say that $\operatorname{\mathcal{C}}$ is cocomplete if it admits $K$-indexed colimits, for every small simplicial set $K$.
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