Everytime the “go learn category theory if you want to become a better programmer” trope arises on HN (less often than it used to, but still occasionally) I’m left scratching my head. I actually learned category theory as a math grad student, before changing fields and going in a more applied direction. I’ve spent decades writing software since then, and I can easily think of about 10 areas of math and CS that are way more useful day to day. Once you’ve mastered calculus, linear algebra, probability theory, statistics, numerical analysis, optimization, algorithms, complexity theory, combinatorics, asymptotic analysis—sure, go pick up category theory.
But Category Theory is different to all the other examples you gave, as it describes program composition. i.e. building larger programs from smaller ones. Computer scientists have been searching for the "mathematics of program construction" for a long time, desperately trying to make the process more formal. Category Theory is what many seem to have arrived at. There are even books about it, e.g. "The Algebra of Programming".
Most computer science graduates are well schooled in algorithms, complexity, linear algebra etc. However, the vast majority of their time commercially will not be spent implementing some core algorithm, but instead gluing systems together and consuming/writing APIs. Any mathematics that helps them better accomplish this would be good to add to their toolbox.
The author of "The Science of Functional Programming" book (https://github.com/winitzki/sofp) makes an argument that CT is at best tangential to practicing FP.
I found category theory to be helpful in giving a vocabulary for some very simple and essential things that otherwise get lost. My goto example are Monoids and Semi-Groups, which are almost mindbogglingly simple but pop up everywhere.
Category theory gives you the precise language to talk about such stuff and helps to communicate and talk about more complex concepts and that's always a plus.
