3 ms·
This is just set theory, not category theory.
by Rerarom 6y ago
This is just set theory, not category theory.
- Garlef 6y agoNeither is more foundational than the other. So I think the use of "just" is not justified here. https://mathoverflow.net/questions/360578/category-theory-and-set-theory-just-a-different-language-or-different-foundati https://mathoverflow.net/questions/360578/category-theory-an...
- deleted 6y ago[deleted]
- nicky0 6y agoBut talking about category theory makes you sound smarter.
- Garlef 6y agoI'm personally more scared of set theory.
- eigenket 6y agoYeah but your comment didn't use the concept of a "category" at all, whereas you used "set" three times. Its definitely more natural to say these definitions come from set theory.
- Garlef 6y agoTo me, "disjoint union", "direct product" and "set of maps" (as a special case of "internal hom") are the central keywords in what I wrote: Concepts from category theory.
- eigenket 6y agoThose keywords all appeared in the context of set theory long before category theory was thought of. Even ignoring that as a historical accident (we invented set theory before category theory), those ideas are all natural, meaningful and interesting to examine in the context of sets even if one has never heard of a category.
- spekcular 6y agoYes, there's no need to invoke any category theory concepts here. Everything is happening in the category of sets.
- spekcular 6y agoFirst, that's not what your link says. (See, e.g., the comments to the first answer.) Second, I find that claim highly dubious. To do metamathematics and talk about the relative strength of various axiomatic systems, you need to talk about large cardinals. So that, at least to me, seems like a good argument that set theory is foundational to mathematics in a way that category theory is not, since the latter has no non-eliminable place in the (study of) contemporary foundations of mathematics.