Is there any ongoing research in category theory?
What's a good school if I want to do a category theory related dissertation?
just learn to draw some arrows and commutative diagrams
>>8034541
Category theory is only a meme.
http://arxiv.org/list/math.CT/recent
Foundations. Everything else is a meme
Category theory without sub-object classifier is like graph theory minus combinatorics. Not much you'd do. If you got them, then you do topos theory, and some look into that.
Homotopy theorist use related language a lot (where its used in a rawer form than in algebriac geometry, say, which also has lots of other structure), though.
>>8034996
You can do a fuck load without topos theory, like say all of type theory.
People don't really do category theory professionally for the sake of category theory. I feel like most of the time it is used to discuss things in algebraic topology or algebraic geometry.
>>8035223
This is somewhat wrong. Algebraic topology is just one of the things category theory is used for. In mathematics it is studied for it's own sake in the form of higher category theory but for the most part if you want to do more category theory you should move to the computer science department, even HoTT is studied in the computer science department.
>>8035430
Higher category theory is essentially being currently pioneered by homotopy theorists, i.e. algebraic topologists.
>>8035687
At my university that's all being done in the computer science department and though everyone has exposure to HoTT only a couple people know homotopy theory itself and are interested in algebraic topology.
I know that people doing logic at my cs school do a lot of category, not sure if that's what you want
>>8034541
some try to answer this
>>8035687
From what I can see, higher category theory is where research is atm. Lurie's book made waves I think, but there are many ways to impose the relations between the n- and m- morphisms in a general way that people study other than the homotopy theorist's way.
http://www.oliviacaramello.com/Unification/AwodeyResponse.html
Daily reminder that even topos theorists believe that topos theory is a meme
Off top of my head:
Harvard
Illnios
Berkeley
>One thing I can say is that I have also felt that the field of topos theory is not a good area for new researchers, in part because some of the experts know a lot more than they have published. Also, there are some people in the field who will easily know almost anything that you can come up with, even if they have not thought of it before, and so you will not get the credit or due respect for even previously unpublished results.
true
>>8037793
what
>>8036526
UIC? Don't know a lot about the math dept. but I have heard good things about CS and logic
>>8036520
Yea, seeing all those responses put me off of topos theory. Instead I went into HoTT and am switching to comp sci where all the real math (type theory) is being done.
