ScalingStacks

Definition 5.2. An $\infty$-category ${\mathcal{C}}$ is $\kappa$-filtered if every map $K\mathchoice{\longrightarrow}{\rightarrow}{\rightarrow}{\rightarrow}{\mathcal{C}}$ from a $\kappa$-small simplicial set $K$ extends to a functor $K^{\triangleright}\mathchoice{\longrightarrow}{\rightarrow}{\rightarrow}{\rightarrow}{\mathcal{C}}$ (see [52, 2.1.4.2] for the cone notation). A simplicial set $K$ is $\kappa$-filtered if there exists a categorical equivalence $K\mathchoice{\longrightarrow}{\rightarrow}{\rightarrow}{\rightarrow}{\mathcal{C}}$ for some $\kappa$-filtered $\infty$-category ${\mathcal{C}}$. Lastly, a $\kappa$-filtered colimit is a colimit indexed by a $\kappa$-filtered simplicial set.