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 mathematici

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) https://en.wikipedia.org/wiki/Monoid_(category_theory) which is a categorification of it.