# Kerodon

$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$

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.