# Kerodon

$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$ $\newcommand\empty{}$

Remark 1.3.0.9. Suppose we are given a filtered diagram of simplicial sets $\{ S(\alpha )_{\bullet } \}$ having colimit $S_{\bullet } = \varinjlim S(\alpha )_{\bullet }$. If each $S(\alpha )_{\bullet }$ is an $\infty$-category, then $S_{\bullet }$ is an $\infty$-category.