# Kerodon

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

Example 2.3.2.4. Let $X_{\bullet }$ be a simplicial set. If $X_{\bullet }$ is an $\infty$-category (in the sense of Definition 1.3.0.1), then every $2$-simplex of $X_{\bullet }$ is thin. Conversely, if every $2$-simplex of $X_{\bullet }$ is thin, then $X_{\bullet }$ is an $\infty$-category if and only if every map of simplicial sets $f_0: \Lambda ^{2}_{1} \rightarrow X_{\bullet }$ can be extended to a $2$-simplex of $X_{\bullet }$.