I studied CS in germany in 1999 and we had "analysis 1+2+3" which I think was a fairly rigorous analysis treatment, I definitely did more than my fair share of proofs. I think that foundation accompanied me through all those years of programming and helped me read and pick up concepts related to type theory, algebra and functional programming.
In parallel I developed this very "visual" way of thinking about structure that makes me really resonate with CT. In a way I'm less interested in learning new maths, more so than learning more about how people approach (complex) structures I already know with these very rudimentary concepts, and seeing how their formalizations match my "folk mathematics".
I'm having a lot of fun!
edit: thanks for the book recommendation! that looks like my kind of maths book
i skimmed through aluffi, and it is indeed exactly the material I had at university in analysis and algebra, augmented with the category theory angle. this is great, thanks a lot. Now I have to find an affordable copy somewhere.
I also like the focus on quotient groups and galois fields, as well as using graphs as recurring examples, which have been the only times I really put the pedal to the maths metal in my programming (for some crypto and error correction stuff).
I can see why categories appeal if you're just looking at definitions, but CT often just abstracts/standardizes an approach that folks were already working with when working with rings, groups, topologies, etc. Going through the proofs will teach you when to apply what.
Aluffi (Algebra: Chapter 0) makes a great book that teaches the basics of CT and brings it up while teaching regular algebra. I highly recommend it.