Kerodon

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

Remark 4.3.4.6. Let $X$ be a locally compact Hausdorff space. Then the functor

\[ \operatorname{Top}\rightarrow \operatorname{Top}_{X/} \quad \quad Y \mapsto X \star Y \]

preserves colimits. This follows from the fact that the functors $Y \mapsto X \times Y$ and $Y \mapsto X \times [0,1] \times Y$ preserve colimits.