Applications of Category Theory Outside of Mathematics (the discipline)

I apologize if this is off-topic, but I wish to know what applications have other disciplines made of category theory. I have heard that linguistics, computer science, and philosophy all make use of category theory. But due either to my own lack of familiarity with category theory or these disciplines, I'm rather ignorant of these applications.

So, what (fruitful) uses have been made of category theory, especially within philosophy, but within other academic disciplines as well?

Solution 1:

As far as I've understood (during my numerous, but small occasions of using) Haskell programming language is heavily based on the category theory. Nonetheless this doesn't mean that Haskell programming needs knowledge of CT, I mean only compiler deeps is "heavy categoric".

A computer science's notion of "type" is the example which can require treatise from a category theory view. It's done this way in Haskell, and it's done similar way in languages like Agda and Coq. These are also a systems of automated proof-checking and proof-assistants and are also heavily (better say "essentially" based on CT). I'm not an expert in this field, just curious, but recent works of Vladimir Voevodsky and The HoTT Book are devoted to subject of further developing CT for proof-checking/assistance purposes.

Solution 2:

In computer science, the monads (aka triples) are closely related to the functional programming monads used, for example, in Haskell. As far as I understand (I'm not an expert), these monads are monads in the category of types and functions.

In physics, higher category theory gives a setting for theoretical physics. It is possible to express many concepts in dynamics, quantum mechanics etc. from the point of view of higher category theory.

Solution 3:

For philosophy, you could read the article on the Stanford Enciclopedia of Philosophy.

Category theory challenges philosophers in two ways, which are not necessarily mutually exclusive. On the one hand, it is certainly the task of philosophy to clarify the general epistemological and ontological status of categories and categorical methods, both in the practice of mathematics and in the foundational landscape. On the other hand, philosophers and philosophical logicians can employ category theory and categorical logic to explore philosophical and logical problems.

This is the beginning of the third section (named philosophical significance) of the article I mentioned. I hope it to be useful for you.