I think Dr. Space's claim that there are a dozen schools where you can do homotopy theory might be true for the United States, but I think it's fair to say that there are a lot of other places in Europe with a plugged-in community (and without a lot of the pomp and circumstance of some of the US schools he might have in mind)

Also, I dunno, Aaron, is the homotopy theory community any worse than the algebraic geometry community?

with the 'obviously'?

I've found homotopy theory people much much more patient and willing to explain points than algebraic geometers 'Have you done all of the exercises in Hartshorne/Vakil's notes??'

Nobody has ever told me to go back and do all of the exercises in HTT…

:D

So anyway, I think we should deflect all of the blame for this onto algebraic geometers.

I hope that was satisfactory to fulfill your expectations of recriminations.

Also I second Denis on this. There's no reason to be embarrassed about asking stupid questions. It's better to ask them than remain ignorant or confused =)

@HarryGindi i'm not sure what you're trying to say here. if you're trying to make a factual claim that contradicts somebody else's lived experience, then i think you're missing the point.

also, i would strongly disagree with your implicit assertion that we should simply aim to be not the worst subfield of mathematics. (i would guess that you probably know this already, which is why you're being self-consciously facetious about it.)

i'm glad you've had good experiences talking with homotopy theorists, and i'm sorry that you've had bad experiences talking with algebraic geometers. but that certainly does not imply that everyone has had good experiences talking with homotopy theorists. and i think it's an extremely important exercise to reflect on negative feedback, rather than becoming defensive and reflexively shifting blame elsewhere.

@blank_space hey thank you for sharing this. I also think I am "homotopy-adjacent" in the sense that the techniques I know and the questions I am interested in are not really part of the "mainstream" (whatever that means). I'd be happy to learn more homotopy theory with you (at ANY level) if you wish. Feel free to email me if you want to talk math. You can feel comfortable asking any kind of questions with me (I am sure many people in this chat feel similarly). :)

Hi, Does anyone know a reference for an explicit proof of the following fact: If X is a simplicial set with a single vertex then |G(X)|, the geometric realization of the Kan loop group of X, is naturally weakly equivalent - as a topological monoid - to the space of Moore based loops in |X|, the geometric realization of X. I have an outline for a proof constructing an explicit zig-zag and some of the combinatorics seem to be surprisingly tricky- I did not find this in the literature.

I guess you can also deduce this by comparing the right adjoints for the functors I just mentioned, perhaps one may find it in this form in the literature.