This might be an unpopular opinion, but category theory isn't very useful at low levels of abstraction. It is an elegant mental framework/model that can be used to generalize many concepts, but in my experience such generalizations rarely give additional insights about the concept it is generalizing.

Seven Sketches in Compositionality by Spivak and Fong (https://math.mit.edu/~dspivak/teaching/sp18/7Sketches.pdf) is supposed to be very practical. It includes many examples, but I'm not sure how useful category theory actually is in the example cases.

There is the theory of monotone co-design (https://co-design.science/index.html) which is formulated using category theory. It seems pretty practical.

Then there's topological data analysis, which is clearly a practical subject, and can be formulated in terms of category theory: https://en.wikipedia.org/wiki/Topological_data_analysis

I'm not very knowledgeful of any of these subjects, but I, like you, got somewhat interested in category theory and tried to find how and where it's used some time ago. These are the main things I found.

This feels to me like "is there any non rubik's cube example of group?". Category theory is a mathematical tool used by mathematicians and built for mathematicians, so you'll have trouble understanding why it's concretely relevant anyway if you're not in the business of doing maths :D The main motivation is that it's a good language for describing some kinds of objects and writing proofs about them.

I'm personaly using category in the field of logic and language semantics (describing and proving stuff about notions of equivalence between programs, results like language X can interpret language Y with such and such fidelity). At a high level, i think category theory is useful in that realm because it enables to make up new structures (algebraic structures, think some set with operations and laws) which will be specific to you (won't be something well known like ring or whatever) but thanks to category theory you'll already have results on these structures because you'll show that they have some generic constructions.

In general category theory sometimes enables mathematical statements to drastically cut down on unimportant assumptions, getting at the real core of some theorem. By doing that, you're enabling other to reuse some result in settings which are "kinda similar", where "morally stuff work in the same way", but where the classical definition would have been too rigid.

edit: concretely about these generalizations: if you know about monoids, then look at https://en.wikipedia.org/wiki/Monoid_(category_theory) which is a categorification of it.

I feel like Scott Wlaschin uses an effective model of teaching concepts closely related to category theory without intimidating learners with mathematical definitions and verbiage. Railway oriented programming is a good example.[1]

My personal opinion is that category theory's main contribution to computer science is aiding composability in strongly typed languages in a type-safe, elegant manner. In the end, software is about breaking down a problem into smaller pieces, implementing and testing them, and them putting the pieces back together. Concepts from category theory provide a rigorous foundation for such compositions.

[1] https://fsharpforfunandprofit.com/posts/recipe-part2/

Cambridge Quantum Computing applies Category Theory to development of quantum computing algorithms. Recent paper by Bob Coecke: https://arxiv.org/abs/2110.05327. Look up more papers by Bob Coecke and co-authors on Arxiv.

Cambridge Quantum Computing and Honeywell Quantum Solutions recently merged to form Quantinuum. I work on the hardware side at Quantinuum. I don't actually use or apply Category Theory on a day to day basis but I know it is useful.

I find it most useful as a kind of conceptual organization. It's not something you'd directly solve problems with, but rather a way of organizing your work on the solutions. In that sense, it's much like software architecture -- you don't directly solve problems with architecture, either, but you do want an architecture that supports you when you need to make changes or grapple with a large or complex problem domain.

Unfortunately, that's also why most resources directly on category theory are deeply wedded to pure mathematics -- it's an architectural form that has been developed by mathematicians to organize their own constructions. Folks like Scott Wlaschin [0] and Mark Seemann [1] have, I think, much more success in teaching categorical concepts in a software context, but since their material is often so far removed from category theory "proper" (intentionally and for good reason), they don't really paint much of a path toward category theory themselves.

(I've recently been learning Agda, a dependently-typed language / proof assistant, and it's kind of shocking how often refactoring my proofs lead to more "obviously categorical" concepts. I really think there's something to this category-theory-as-mathematics-architecture angle.)

[0] https://fsharpforfunandprofit.com/rop/

[1] https://blog.ploeh.dk/2017/11/13/endomorphism-monoid/

I wrote this article[0] as part of my own journey to understand monads and category theory.

I think you may find it helpful. It has a practical use case that builds up an intuitive model to a new monad. It goes through a few solutions for a stated problem which solve increasing requirements and eventually coalesces into writing a new monad as a complete solution to resolve all the built up requirements.

[0] https://sambernheim.com/blog/building-a-monad

This series has some C++ examples alongside Haskell: https://bartoszmilewski.com/2014/10/28/category-theory-for-p... and acquirable as a PDF at https://github.com/hmemcpy/milewski-ctfp-pdf