5 ms·

I think this is a rather peculiar comment — category theory is interesting precisely _because_ it's closely connected to other branches of mathematics, and can

by Twey 3y ago

I 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 ago
Well, we disagree here.
- Twey 3y ago
  I 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'.
    - Twey 3y ago
      I see — so it seems like what confused me about your comment is that your definition of ‘closely connected’ doesn't mean in a theoretical sense, i.e. that there's a well-understood mapping between them, but is more about a cultural connection in which people make choose to make active use of category-theoretical concepts when working in a more concrete field? Thank you for explaining :)

by Twey 3y ago

deleted 3y ago

[deleted]

bmacho 3y ago

Well, we disagree here.

Twey 3y ago
I 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'.
  - Twey 3y ago
    I see — so it seems like what confused me about your comment is that your definition of ‘closely connected’ doesn't mean in a theoretical sense, i.e. that there's a well-understood mapping between them, but is more about a cultural connection in which people make choose to make active use of category-theoretical concepts when working in a more concrete field? Thank you for explaining :)