Kerodon

Variant 9.1.1.4. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category and let $\kappa $ be an infinite cardinal. We say that $\operatorname{\mathcal{C}}$ is $\kappa $-filtered if, for every $\kappa $-small simplicial set $K$, every diagram $f: K \rightarrow \operatorname{\mathcal{C}}$ admits an extension $\overline{f}: K^{\triangleright } \rightarrow \operatorname{\mathcal{C}}$. We say that $\operatorname{\mathcal{C}}$ is $\kappa $-cofiltered if the opposite $\infty $-category $\operatorname{\mathcal{C}}^{\operatorname{op}}$ is $\kappa $-filtered.