Kerodon

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

Definition 1.1.6.1. Let $S_{\bullet }$ be a simplicial set and let $S'_{\bullet } \subseteq S_{\bullet }$ be a simplicial subset of $S_{\bullet }$ (Remark 1.1.2.4). We will say that $S'_{\bullet }$ is a summand of $S_{\bullet }$ if the simplicial set $S_{\bullet }$ decomposes as a coproduct $S'_{\bullet } \coprod S''_{\bullet }$, for some other simplicial subset $S''_{\bullet } \subseteq S_{\bullet }$.