I'm trying to learn category theory. It's not the kind of thing you can learn the way this article suggests. I find learning new abstractions rather difficult especially at the level of category theory. If anyone has any tips I'd love to hear them.
If abstracts algebra is too difficult then learn introduction to proofs before continuing with abstract algebra.
Try doing problems and posting them online to have them checked. Currently you can use discord, reddit, math stack exchange etc
Don’t worry about rushing it. Everything builds on itself. For instance once you rigorously study introduction to proofs you’ll see the same sort of proofs again when you begin studying abstract algebra and will already be familiar with the concepts.
supplement those books with these lecture videos:
https://youtube.com/playlist?list=PLl-gb0E4MII28GykmtuBXNUNo...
they appear to follow rosen but they’re the same topics you’d see in epp
if you’re the complete beginner go with epp and then use rosen as a supplement.
if you are an advanced undergraduate in math but don’t know category theory then:
https://math.jhu.edu/~eriehl/context.pdf
or
Basic Category Theory by Tom Leinster
(even though i’ll list a bunch more resources below i’d probably start with leinster and work up enough math maturity to push through it.)
i also liked this: https://arxiv.org/pdf/1912.10642.pdf
if you don’t know advanced math then there is an upcoming (not yet released book) called “the joy of abstraction”
i cannot attest for the book as i haven’t read it but may be good for true beginners:
https://www.cambridge.org/us/academic/subjects/mathematics/l...
(click “look inside”)
they say “no formal mathematical background needed”
you can read the description and see if that is something that would be of interest to you.
this guy has videos + a book
there are a lot of books like “category theory for programmers”, “programming in categories” and the “seven sketches” books along with lecture recordings and videos that you may find helpful.
category theory for programmers might be the easiest of those three books. i worked a bit out of the programming with categories (http://brendanfong.com/programmingcats_files/cats4progs-DRAF...) book and ignored all the haskell sections and just focused on the math parts (this is a distinct book from “category theory for programmers”. people confuse the two due to the names and the fact they both use haskell).
if you know category theory and want to learn topology then there is “ Topology A Categorical Approach” by bradley et al.
https://www.youtube.com/watch?v=ho7oagHeqNc
and in a similar vein I am enjoying her book: "How to Bake Pi".
Getting more into the technical side of things, Bartosz Milewski has good lessons in this playlist:
https://www.youtube.com/watch?v=I8LbkfSSR58&list=PLbgaMIhjbm...