[nimithryn]

Look into OpenCog - there's some sheaf-theoretic NLP stuff going on there. There's a recent high-level overview by Linas Vepstas you can find on the ArXiv somewhere. There's a project called SheafSystem also, which is a sheaf-based database for scientific computing (I've never used it). I have some ideas I'm working on in this area also (not affiliated with these parties in any way, and the ideas are not ready to share yet, unfortunately.

What's your background, out of curiosity?