Real world applications of category theory

Question

I was reading some basic information from Wiki about category theory and honestly speaking I have a very weak knowledge about it. As it sounds interesting, I will go into the theory to learn more if it is actually useful in practice.

My question is to know if category theory has some applications in practice, namely in engineering problems.

I have already read this Applications of category theory and topoi/topos theory in reality

and the answers are only about programming which are not very interesting from my point of view.

Any comments are welcomed, thanks in advance.

Answer 1

Category theory is far from the engineering textbook level, for now. On the research level, there are a lot of instances where category theory is applied in engineering context, from electrical to biomedical engineering. Beware though: these usually come from people who try to apply category theory, rather than from people who try to solve an engineering problem and find category theory useful in doing so.

Answer 2

Category theory is a good and powerful language capable of expressing various concepts of purely algebraical nature.

But it is a terrible tool for actually solving problems.

To convince yourself that the last statement is true try to think about a proof of a theorem from another branch of mathematics that depends on a category theory in a crucial, non-linguistic way. I doubt you will find any such proof. Thus it is hardly a surprising fact that you will not find any serious application of category theory in engineering problems.

On the other hand, you will find plenty of applications of category theory inside category theory. Category theory fights with problems originating in category theory, with problems of no practical relevance for mathematicians, not to mention engineers.

Answer 3

Seeing how software has infiltrated our lives in so many ways it seems that category theoretic applications to programming is pretty much 'real world' stuff.

Category theory is more geared up to clarifying conceptual structures, so I imagine that there isn't likely to be real world applications in a very direct way soon, and I say this as some-one who likes the general theory.

Answer 4

I recently wrote some software to simulate a real world physical system to show that a hardware technology has a chance of doing what we want it to do. That project has grown to a pretty substantial piece of engineering with sizable budget. I wrote the simulation in a programming language whose syntax could be described as the "internal language" of a Cartesian closed category with a bunch of extensions, many of which were categorically motivated.

Sadly I eventually had to switch to Python because I couldn't find libraries for everything I wanted.

The language was Haskell.