Honestly I'm pretty weak in both, but they seem to reflect my intuitions, if that makes sense? I'm nowhere near a working mathematician, and proofs usually bore me. I prefer writing code.
If you're looking for an alternate perspective, I would suggest taking an advanced undergraduate analysis book and working through it, proofs and all. It'll teach you the same kinds of stuff that you're getting out of CT but will give you "working" (lol) knowledge of how to apply it. A lot of mathematical work is about creating math objects and relations and proving properties of these objects through their relations. The exercises in a good algebra book will exercise this muscle and make your software organization better, at least IMO. Learning the definitions just isn't a substitute.
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.
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).
