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Variant 7.2.4.4. Let $\operatorname{\mathcal{C}}$ be an $\infty$-category. We say that $\operatorname{\mathcal{C}}$ is cofiltered if, for every finite simplicial set $K$, every diagram $f: K \rightarrow \operatorname{\mathcal{C}}$ admits an extension $\overline{f}: K^{\triangleleft } \rightarrow \operatorname{\mathcal{C}}$. Equivalently, $\operatorname{\mathcal{C}}$ is cofiltered if the opposite $\infty$-category $\operatorname{\mathcal{C}}^{\operatorname{op}}$ is filtered.