6,223 reputation
1336
bio website people.mpim-bonn.mpg.de/…
location Bonn
age 32
visits member for 4 years, 1 month
seen Apr 8 at 19:48

I am a postdoc at the Max Planck Institute for Mathematics. I did my PhD at Utrecht University under the advisement of Ieke Moerdijk. My thesis was entitled "Categorical Properties of Topological and Differentiable Stacks". My current research interests are applications of higher category, derived geometry, and recently field theory.


Mar
10
awarded  Yearling
Nov
28
comment What properties do “large topoi” share with actual topoi?
Thanks, this is a nice way of thinking :)
Nov
28
accepted What properties do “large topoi” share with actual topoi?
Nov
28
comment What properties do “large topoi” share with actual topoi?
Ah- well, I suppose one needs the caveat that $\mathcal{A}$ is also locally small, which a big group is not.
Nov
28
comment What properties do “large topoi” share with actual topoi?
By the way, in light of Todd's answere here: mathoverflow.net/questions/24540/… it seems $[\mathcal{A}^{op},\mathbf{Set}]$ is only locally small if $\mathcal{A}$ is essentially small.
Nov
28
revised What properties do “large topoi” share with actual topoi?
edited title
Nov
28
comment What properties do “large topoi” share with actual topoi?
Thanks Zhen for the nice answer. Could you perhaps recommend a good reference?
Nov
28
revised What properties do “large topoi” share with actual topoi?
added 18 characters in body
Nov
28
asked What properties do “large topoi” share with actual topoi?
Nov
28
comment Local smallness and (higher) topoi
@AntonFetisov: P.S. If you send me an email (so I have your email address), I will send you an email when the preprint appears on the arxiv (which will be very soon).
Nov
28
accepted Local smallness and (higher) topoi
Nov
28
comment Local smallness and (higher) topoi
@AntonFetisov: Thanks for the updated answer!
Nov
28
comment What does it mean for a Deligne-Mumford stack to have trivial generic stabilizers?
@user76758: For a topological etale stack, each point $p$ (and here I mean point in the sense as a map from the one point space), factors through an etale atlas $X \to \mathscr{X}$ from a space, and the automorphism group $Aut(p)$ acts on the germ around $p$ of $X$. The etale stack $\mathscr{X}$ is effective if and only if each of these actions is faithful.
Nov
28
comment What does it mean for a Deligne-Mumford stack to have trivial generic stabilizers?
@user76758: It is more geometric yes, but I was just checking that I understood the definition correctly, as there was a lot of terminology in your comment. Do you perhaps know the answer to the question I posted as the comment to the answer below btw?
Nov
28
comment What does it mean for a Deligne-Mumford stack to have trivial generic stabilizers?
Thanks, this is the kind of example I was certainly expecting for something with non-trivial generic stabilizers. Can I make precise the following idea? : $\mathscr{X}$ has trivial generic stabilizers if and only if "each point $p$ has $Aut(p)$ acting faithfully"? This is the situation that occurs in the topological context.
Nov
28
comment What does it mean for a Deligne-Mumford stack to have trivial generic stabilizers?
@user76758: Thanks for your response. So, if I am understanding you correctly, in particular, is the following equivalent to $\mathscr{X}$ having "trivial generic stabilizers"? : There exists an \'etale atlas from a scheme $X \to \mathscr{X}$ such that for each generic point $p$ of $X,$ the stabilizer of $p$ in $\mathscr{X}$ is trivial?
Nov
27
asked What does it mean for a Deligne-Mumford stack to have trivial generic stabilizers?
Nov
26
comment Local smallness and (higher) topoi
@AntonFetisov: I will re-accept your answer if you can explain to be why there is a non-small category of models. I don't quite see it. Thanks!
Nov
25
comment Local smallness and (higher) topoi
@AntonFetisov: Wait- why is there a non-small category of models in $\mathcal{E}/E$? I assume here that $E$ corresponds to the etale map $L\to L \coprod pt$?
Nov
14
comment Which dense inclusions of sites are ∞-dense?
In that case, as long as your infinite-dimensional manifolds are locally modeled on "convenient vector spaces" (e.g. Frechet spaces), then $f$ is infinity dense. I'm a bit busy this moment, but I will try to type up the proof soon.