I’m cautiously optimistic about applications of category theory. I believe category theory has the potential to be useful, but I’m skeptical of most claims to have found useful applications. Category theory has found useful application, especially behind the scenes, but a lot of supposed applications remind me of a line from Colin McLarty:
[Jean-Pierre] Serre created a series of concise elegant tools which Grothendieck and coworkers simplified into thousands of pages of category theory.
To be fair, Grothendieck put these recast tools to good use, but most mere mortals would stand a better chance of being able to use Serre’s versions.
My interest in category theory waxes and wanes, and just as it was was at its thinnest crescent phase I ran across CQL, categorical query language. I haven’t had time to look very far into it, but it seems promising. The site’s modest prose relative to the revolutionary rhetoric of some category enthusiasts makes me have more confidence that the authors may be on to something useful.