I'm layman to Category theory. Trying to understand it, I just read a bit briefing on it and wiki pages of Category, Functor, Morphism. However I still could not see the merits of it.
Category theory, in layman's eyes, is another layer of abstract, similar to abstract algebra's group, ring, field or set theory's induction, poset, well-ordering. Now, after the abstraction, what's the benefit?
A possible benefit that I could imagine, is that it might bypass some restriction on algebra or set theory? for example set theory talks about "set", maybe Category Theory can talk about "class"? or, algebra talks about "group", this is again based on set, so Category Theory can talk about "group-like categories"? so maybe some results in set theory or algebra can be generalized? for example algebra talks about groups, saying that left $e$ and right $e$ is the same, and left inverse and right inverse of an element is also the same, maybe this could be generalized in Category Theory?
Anyway, could you give some examples of useful Category Theory results (theorems or approaches) that could be used in other more "concrete" mathematics fields?