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1,000quite long but extremely clear and my favourite source
https://www.youtube.com/@RichardSouthwell
The guy has a book, would check that out, though it wasn't online when I searched for it around 1.5 years ago
if you're gonna read a textbook, get ready to spend an hour on a single page.
Do not recommend Steve Awodey's book, it is concise at the expense of clarity, though it does have good diagrams, and if you get it, then the concision looks good lol. But these set of 4 lectures by him are okay as an intro:
https://www.youtube.com/watch?v=BF6kHD1DAeU&list=PLGCr8P_YncjVjwAxrifKgcQYtbZ3zuPlb
Emily Rhiel's and categories for the working mathematician are good, but hard, so I don't recommend them either.
There's various other books I haven't read titled "introduction to category theory" or similar, which are probably much better for a first introduction. Now that I think about it, maybe if I'd read these instead I wouldn't have had to spend an hour on a single page lol
Applied category theory: never looked at these lectures or his book, but I probably should have, so I didn't get stuck in armchair theory land, which is very easy to do in category theory. I think this is also what johnswentworth recommends:
https://www.youtube.com/watch?v=UusLtx9fIjs&list=PLhgq-BqyZ7i5lOqOqqRiS0U5SwTmPpHQ5
To that end, you could probably also look at books titled as "for computer scientists"
In general, there's like a few key categorical concepts you'll see, and the best thing to do is probably to look at multiple sources until you get it
Misc:
Lawvere's conceptual mathematics is basic, but has some interesting ways of looking at things; I summarize a few of the most interesting of them here:
https://www.overleaf.com/project/63860d18f52aa6c2e821e3f4
This paper is good for getting exposed to the idea of string diagrams:
https://arxiv.org/abs/1401.7220
This channel has some short video proofs, as a supplementary source
https://www.youtube.com/user/thecatsters
The first chapter of Aluffi's "Algebra: Chapter 0" is an excellent and friendly introduction to category theory. I learned it using it myself at the start of a course in abstract/modern algebra (as in finite fields, not the quadratic equation), and I highly recommend it. IIRC you can even find it for free online.
Having 3k mana was too much for me so I boosted this and upped the bounty because this is relevant for me too. I know bits of category theory and I’ve nibbled math in various places for years but I’m unfocused and so I look for a magic bullet. Probably slow and steady bit by sporadic bit learning from random sources will do me good even without structured learning materials but a man can dream.
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