Reddit reviews Categories for the Working Mathematician (Graduate Texts in Mathematics)

Categories for the Working Mathematician. Of course, that's geared more towards people who need some category theory in their own work. Category theory by itself is like a bookshelf. A nice way to organize your stuff, but nothing substantive is actually there until you fill it with books.

Depends on your background. Mac Lane is the standard text and he is a phenomenal author in general, but it builds off knowledge of concepts such as modules, tensor products and homotopy (I still don't have a sufficient background in AT to be honest though). For a more modest background, I would recommend the book "Sets for Mathematics" by Lawvere and Rosebrugh. The book is entirely on category theory, the title is because there is a focus on the category of sets. The first chapter or so is deceptively simple, it gets very difficult as it goes on, but still doesn't require much specific background.

I'll also note that I first got into the subject through a whim purchase in a local Borders of a cheap dover book Topoi by Robert Goldblatt when I was very into mathematical logic. It's 500 pages and requires pretty much no background (I'd know what a topological space is, but I can't think of anything else). It gets very challenging though, and I never got more than 250 pages in before getting overwhelmed, but the first hundred pages really sparked my interest in category theory. Functors (and especially adjoint functors) are postponed much later than you will see in many other sources though. You can find a link to an online version free from the author's webpage too.

I do not know of any category theory texts I'd say would be accessible to undergrads. But if you are really interested, you might try the first chapter of these very excellent notes due to Ravi Vakil. Someone is probably going to jump down my throat for suggesting these to you (they are considered pretty challenging), but they will give you a good idea of the flavor of category theory. If you are really, really interested in category theory and you have a professor/ grad student you can talk to about these notes, you could really learn a lot here. Another book I hear about a lot is this one but I have never used it myself.

Ok, but really, starting with Ravi's notes might be a little too much. I actually suggest this youtube channel as your first foray into trying to learn category theory. The lectures are fairly accessible and you can always pause them, go back, etc.

If you are really, truly, interested in learning more about category theory, my suggestion is to go to your professor and ask about it. You do not have to be enrolled in a class about category theory to learn it, and this could be a great springboard into some sort of honors project for you. Good luck!

Edit: Ozob beat me on the MacLane! It's also worth noting that, depending on your institution, you may be able to view Springer books for free/ buy them for cheap. Ask your department.

Categories for the Working Mathematician

Yeah, I've just never been shown a problem where this stuff gives deep insight, and until I see one and understand it these are just gonna be arbitrary definitions that slide right out of my brain when I'm done reading them. I'll definitely give the book a look - is it motivated with examples?

The only book I have on category theory is Conceptual Mathematics: A First Introduction to Categories, and I must say, I'm not a fan of it - too intuitive, not detailed enough, not well organized, not formal enough - should have gone for MacLane instead.

There's a lot of category theory, but this only uses the basics. Galois theory is deeper than anything used so far. Category, functor, natural transformation (co)limit, and maybe adjoint should be plenty (it looks like gibbon's tries to explain everything about adjoints that he uses). That's all in the first four or five (short) chapters of MacLane.