A simple (but potentially dangerous) question - is there any practical application of category theory?
(I have PhD in quantum physics theory... yet, each time I see category theory, it looks to me as abstract nonsense. The only example when it was for me anyhow insightful is the abstract definition of tensor product; but for more mundane stuff, all examples I know can be implemented with functions (or even: matrices :)).)
The prime purpose of CT is unification, showing that many familiar things are instances of the same idea. In that sense CT is shallow, you can always in principle do without CT what you can do with. But without the abstract view afforded by CT, you may not see similarities.
Here are moderately practical things that came from CT.
- CAML, the predecessor to OCaml had a virtual machine based on category theory.
- Monadic effect handling, which is an approach to modularising computation, is based on category theory.
- Remarkably, Bell's theorem from physics and database theory share a surprising amount of structure, see [1].
- Modern libraries like Scala's Scalaz.
[1] S. Abramsky, Relational Databases and Bells Theorem.
(I have PhD in quantum physics theory... yet, each time I see category theory, it looks to me as abstract nonsense. The only example when it was for me anyhow insightful is the abstract definition of tensor product; but for more mundane stuff, all examples I know can be implemented with functions (or even: matrices :)).)