Kerodon

$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$

Definition 1.3.0.1. An $\infty $-category is a simplicial set $S_{\bullet }$ which satisfies the following condition:

$(\ast '')$

For $0 < i < n$, every map of simplicial sets $\sigma _0: \Lambda ^{n}_{i} \rightarrow S_{\bullet }$ can be extended to a map $\sigma : \Delta ^{n} \rightarrow S_{\bullet }$.