Definition 10.1.1.1. Let $K$ be a simplicial set. We say that $K$ is sifted if, for every finite set $I$, the diagonal map $K \rightarrow K^{I}$ is right cofinal. If $\operatorname{\mathcal{C}}$ is an $\infty $-category, we say that a diagram $K \rightarrow \operatorname{\mathcal{C}}$ is sifted if the simplicial set $K$ is sifted.
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