Kerodon

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

Remark 1.1.7.3. The functor $X \mapsto \operatorname{Sing}_{\bullet }(X)$ carries limits in the category of topological spaces to limits in the category of simplicial sets (in fact, the functor $\operatorname{Sing}_{\bullet }$ admits a left adjoint; see Corollary 1.1.8.5). It does not preserve colimits in general. However, it does carry coproducts of topological spaces to coproducts of simplicial sets: this follows from the observation that the topological $n$-simplex $| \Delta ^ n |$ is connected for every $n \geq 0$.