> category theorists tend to turn up, simply name things that other people have spent their lives working on
A lot of category theory (at least the more basic parts thereof) is about bringing together concepts that were isolatedly worked on in very different mathematical communities and formulate them in a unified way so that one can see a unifying pattern that was hardly visible before.
> What practical problems can I solve with it?
If you simply want to work on some topic/problem of your interest, category theory will likely be of limited help (except perhaps for finding a more elegant formulation of the things that you work on). If, on the other hand, you seek deep relationships between topics that to most people look unrelated, getting deeply into category theory is likely not a bad idea.
Thus: "from the perspective of someone who is interested in solving practical problem", category theory gives you rather little new problem solving techniques by itself. But category theory gives you a cool lookout to perhaps enable you to apply solution techniques from other areas, where without category theory you would not be able to see the relationship between the technique from a seemingly unrelated area and your problem.
A lot of category theory (at least the more basic parts thereof) is about bringing together concepts that were isolatedly worked on in very different mathematical communities and formulate them in a unified way so that one can see a unifying pattern that was hardly visible before.
> What practical problems can I solve with it?
If you simply want to work on some topic/problem of your interest, category theory will likely be of limited help (except perhaps for finding a more elegant formulation of the things that you work on). If, on the other hand, you seek deep relationships between topics that to most people look unrelated, getting deeply into category theory is likely not a bad idea.
Thus: "from the perspective of someone who is interested in solving practical problem", category theory gives you rather little new problem solving techniques by itself. But category theory gives you a cool lookout to perhaps enable you to apply solution techniques from other areas, where without category theory you would not be able to see the relationship between the technique from a seemingly unrelated area and your problem.