5 ms·
A pretty obscure branch of mathematics? You've got to be kidding me. I don't understand HN's fetish for category theory either, and I find it rather weird - I'l
by uxp8u61q 3y ago
A pretty obscure branch of mathematics? You've got to be kidding me. I don't understand HN's fetish for category theory either, and I find it rather weird - I'll refrain from even less charitable words. But as an actual professional mathematician... no, it's not an obscure branch of mathematics.
You don't believe me? Read the ICM proceedings https://www.mathunion.org/icm/proceedings https://www.mathunion.org/icm/proceedings and count how many times the words "category" or "functor" appears. And notice something very special, too: you'll find articles that are not about category theory per se, and that will still mention categories. And you know what? They don't even explain what they are. You know how that can be? Categories are so pervasive in mathematics. You wouldn't write an article for the proceedings and explain what a group or a vector space is, would you? Well, same for categories. It's a basic (in the original sense of the word) part of mathematics.
- bmacho 3y agoCategory theory is not the definition of categories.
- uxp8u61q 3y agoUh?
- bmacho 3y agoThey use the word "category" instead of set, and the word "functor" instead of homomorphism. Category Theory is still very-very obscure, with little to no connection to the rest of mathematics.
- uxp8u61q 3y agoNo, and no.
- Twey 3y agoI think this is a rather peculiar comment — category theory is interesting precisely _because_ it's closely connected to other branches of mathematics, and can be used as a lingua franca to translate concepts and discoveries between them.
- deleted 3y ago[deleted]
- bmacho 3y agoWell, we disagree here.
- Twey 3y agoI made the comment — and find yours interesting — because the usual criticism is CT is the opposite, that it provides new language for accomplishments in other fields of mathematics but offers little in the way of novel results itself: a great quote I heard once is that ‘category theory is great for telling you what you've done’ :) So I'm curious as to how exactly you disagree: the existence of connections between CT and other fields are objectively and verifiably well established (just read a randomly-selected CT paper!) but perhaps you feel like the categorifications of other fields are incomplete or unrepresentative? Or that the connections are in some sense forced or unnatural?
- deleted 3y ago[deleted]
- bmacho 3y ago> So I'm curious as to how exactly you disagree: the existence of connections between CT and other fields are objectively and verifiably well established (just read a randomly-selected CT paper!) I don't think that there are as many and as important as they claim, and I don't think that several fields use them (yet). Sure, CT advocates have huge lists of unifications and connections (e.g. categories for the working mathematician has a lot), but they don't appear on the other side. Maybe they will, but I don't think they do yet. Thus the 'obscure'.