Hello,
Limited category intersection as part of the API would be extremely useful for wikis with overlapping categories. I discussed this on IRC with Simetrical, and it seems that limiting intersection to categories of 5000 or less members each should not use excess resources for a bot API (although benchmarks would be needed).
PHP intersection of very large categories took me less that one second (with longer times to retrieve category members before intersection) using a PHP script. It should be faster in SQL, since it retrieves and intersects simultaneously.
The SQL query itself should be relatively simple. The URL query might look something like the following, which would also make union (list of all pages in either category) possible by changing &return. http://en.wikisource.org/w/api.php?action=query&list=categorymembers&...
Does this seem feasible? I could try my hand at coding it if nobody else will, but I have only a patchwork knowledge of PHP and SQL.
Yours cordially, Jesse Martin (Pathoschild)