In <https://mathoverflow.net/questions/195248/co-hausdorffification>, it is mentioned that the subcategory of **Top** consisting of Hausdorff spaces is not closed under colimits.

The simplest colimit I could think of is the disjoint union, but this doesn't appear to provide a counterexample.

*What is an example of a colimit of Hausdorff spaces which is non-Hausdorff?*