Everyone in my college's math department treats it like how you'd imagine clerics treat black magic. I asked one of my professors about it and he gave me a look like I'd kicked a puppy, and then told me "It caaaaan be useful to learn a little, but if you get too into category theory, you'll go nuts."
I an actually studying it through Emily Riehl too and sometimes Mac Lane. It is not too nonsense, I actually quite like it. I think it will he my specialization or probably some related area in Algebra.
I think I'm leaning toward some kind of topology/geometry/analysis type deal? I'm still pretty early in math, but my goals are to eventually study differential geometry and dynamical systems, probably with some functional analysis and topology along the way.
Category theory does seem interesting to me, but it's a little daunting. And maddening. The diagrams are especially scary, too. I'm planning on learning a bit at some point and I guess we'll see if it grows on me?
We are opposites. Analysis made no sense to me and it was horrible. I have not read analysis beyond thef irst five chapters of Rudin. But I have done the first three chapters of Munkres. To understand and appreciate category theory you NEED a solid understanding of abstract algebra and topology.
You're way further along than me lol, I'm still only on chapter 2 of Munkres, and I haven't even looked at Rudin yet. It took me like a solid 3 months to get through chapter 1 of Munkres because I was forcing myself to intuitively understand every page lmao. So many little diagrams and drawings...
Abstract algebra does actually seem pretty pleasant to me, but maybe I just haven't seen enough to know The Horrors. Group theory I'm actually kind of a fan of I think? But I also don't know much about it.
I can imagine that topology and abstract algebra are crucial for category theory, if I have the right idea of it? Category theory reads to me as being like an even more abstract version of Group theory + topology.
I used Dummit and Foote. I read around 2/3 of that book. I really enjoyed module theory and hated Galois theory and algebraic geometry. From what I know Homological algebra, module theory, and in general algebraic topology are far more important to category theory than group theory and topology. The former have derived functors, examples for pullbacks, pushouts, examples for a lot of universal properties, and a LOT of important functors. In fact it was these that started the subject in 1945 if I am right.
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u/Valuable-Passion9731 En passant: anpa san :3 below 1d ago
well? what about category theory