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Jocelyn Ireson-Paine (Jan 10 2025 at 20:58):My program at http://www.j-paine.org/cgi-bin/webcats/webcats.php is working once more, and can draw and explain diagrams of products, coproducts, equalisers, pushouts, and other constructs. Like these:
To use it, go to the URL, and you'll see some explanation followed by an HTML form. This invites you to choose a construct and optionally give sets and arrows to build it from it. If you don't, it will choose them at random. Then press Submit, and you'll get a green message saying "Your results are here". This is a link which, if clicked, will load the results page. Typically, this page centres around one or two diagrams. These exemplify the construct, and perhaps explain some property such as non-uniqueness.
Background is that this is a program I wrote in 2008 or 2009. It's been on my site since, but almost certainly stopped working last January after the hosting company moved to a new server. The program is written in Prolog, and it seems they forgot to copy their Prolog compiler over to the new server. I just found this out and have been fixing the damage.
There are still problems, I think. The program also calls GraphViz, to make the diagrams. Both that and Prolog have skipped several generations, and don't seem entirely compatible with the older versions I wrote the code for. Some diagrams are now wildly out of scale, for instance, and I think there's a bug to do with Prolog's sort predicate. The program sometimes also crashes if it runs out of space for GraphViz files, which happens if I can't afford to buy more filespace. If you notice such things, please report them in this thread.