Re:Computational Category Theory in Python III: Monoids, Gro...
by WoahNoun on Monday May 04, 2020 @03:34PM
(#23072328)
I love Hatcher's book so I can't disagree with you. (Although he does have a section on category theory in chapter 2, but never revisits it again). But doing anything with sheaves and schemes without categories would feel a lot like doing linear algebra without matrix notation and just using lots of double sums. I also have a copy of JP May's a Concise course in Algebraic Topology next to me and I also love the presentation there. (Although I would absolutely never want to use that book as a first course haha. Hatcher is a classic for a reason.)
Being slightly facetious here as obviously Griffiths and Harris uses sheaves extensively and no category theory.
Re:Computational Category Theory in Python III: Monoids, Gro...
by spekcular on Monday May 04, 2020 @04:04PM
(#23072646)
Yeah, I totally agree.
It's just I see a lot of category hype on here and I want to yell that it's mostly just linguistic! It's not some deep or scary thing. The analogy to matrix notation is really good.
Re: Aluffi, it's a fine book, but I'm not sure I'd teach it that way, because I'm not sure what introducing universal properties and so on really buys you at that level. I guess it make sense if you commit to getting to the end with the abstract perspective on homological algebra. But for a grad student just looking to pass his or her quals? The discussion in Hatcher is concrete, motivated, and involves zero category talk.