@dirkt 12d
I've also seen this in many books.

When I learned it at university, we had lots of examples, but you need to be already familiar with a lot of somewhat abstract mathematics (monoids, groups, rings, sets, homomorphisms, ...) before you see how it unifies those.

Category theory is called "general abstract nonsense" for a reason.

You can think of it as "expressing other mathematics in terms of arrows and commuting diagrams".