[_dps]

I share your view of what working mathematicians think like on this subject. I summarize it thus: how many interesting theorems are there in Category Theory? And the answer you get from proponents varies, but it seems to be like 1-3 with some being kind of a stretch. I would love to learn of a body of theorems like those of analysis or topology or algebra, but by comparison there seems to be very little "there" there. I would be happy to be proven incorrect on this!

[rsj_hn]

Yeah, there's a lot of confusion for people using concepts like morphisms as a notation in their work versus category theory as a research program in and of itself. I don't think there is any research program there. But a lot of the more abstract topics like Motives use this language of morphisms and so people consider that to be category theory as well. I've even heard of people calling all the diagram chasing techniques like spectral sequences category theory, but I have to keep pressing the notation versus ideas distinction and give that a firm "no". If we start organizing mathematical subjects by their notational or bookkeeping systems, then we will not end up with useful categories (so to speak:)).