Kerodon

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

Warning 1.1.7.6. Let $X$ be a topological space. If the simplicial set $\operatorname{Sing}_{\bullet }(X)$ is connected, then the topological space $X$ is path connected and therefore connected. Beware that the converse is not necessarily true: there exist topological spaces $X$ which are connected but not path connected, in which case the singular simplicial set $\operatorname{Sing}_{\bullet }(X)$ will not be connected.