Hello,
I present a proposal for a system that is going to solve the category intersection problem (and, in fact, allow all set-theory operations for categories). The name I suggest for it is “Caterpillar”.
Such a system would consist of a C or C++ backend daemon that stores all the category graph in RAM and MediaWiki extension frontend.
Here is the full text of the proposal: https://www.mediawiki.org/wiki/User:Kalan/gsoc
I am seeking for an interested mentor.
— Kalan