6,763 reputation
1539
bio website people.mpim-bonn.mpg.de/…
location Bonn
age 32
visits member for 4 years, 7 months
seen Oct 21 at 23:20

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.


Sep
30
awarded  Explainer
Aug
26
awarded  Popular Question
Aug
21
revised Nonunital $E_\infty$-rings
added tags
Aug
21
comment Limits and colimits in a 2-category vs. in an infinity category: the non- (2,1)-case
@Zhen: There's lots of examples like this, I was just hoping there was some relation between limits and colimits in the bicategory and in the $(\infty,1)$-category. They certainly won't be the same- that would be way too strong. I'm just wondering if there's any relation at all. shrug?
Aug
21
comment Limits and colimits in a 2-category vs. in an infinity category: the non- (2,1)-case
I'm hoping perhaps that some weighted limits and colimits in the bicategory can be used to get my hands on limits and colimits in the $(\infty,1)$-category, or something along these lines.
Aug
21
revised Limits and colimits in a 2-category vs. in an infinity category: the non- (2,1)-case
added 9 characters in body
Aug
21
comment Limits and colimits in a 2-category vs. in an infinity category: the non- (2,1)-case
@Zhen: I mean bicategorical, not $2$-categorial, so I will edit. And yes, of course $(2,1)$-categorical limits and colimits are the same if I construct the associated $\left(\infty,1\right)$-category simply by taking the maximal groupoid at the level of mapping spaces, but that's precisely what I don't want to do. My construction isn't "incorrect", I'm just after a different thing. I've constructed a bicategory where the mapping categories are supposed to model the homotopy type (via their classifying space) of the mapping spaces in the $(\infty,1)$-category I'm really after.
Aug
21
asked Limits and colimits in a 2-category vs. in an infinity category: the non- (2,1)-case
Aug
13
comment Derived Functors, Projection Formula and Base Change in the Derived $\infty$-Category
May I ask what your motivation is? Without knowing more info, I would guess that this is only a reasonable thing to study if the stack $X$ has an etale atlas, i.e. is an etale differentiable stack (basically an orbifold, but without separation conditions).
Aug
12
comment Derived Functors, Projection Formula and Base Change in the Derived $\infty$-Category
Ok, good (that's the same as a stack of principal bundles btw).
Aug
12
comment Derived Functors, Projection Formula and Base Change in the Derived $\infty$-Category
What do you mean by "smooth stack"? Differentiable stack, i.e. the stack of principal bundles for a Lie groupoid, or something else?
Aug
7
comment Diffeology as a sheaf on the site of smooth manifolds
@Todd: I think a bit more is needed, because we are talking about the $2$-category of psuedo-functors into the $2$-category of groupoids, not the $1$-category of strict functors- but the "more that we need", I explain above, which works not just for groupoids, but for $n$-groupoids for any $n$, even $n=\infty$. But thanks for pointing out that the $1$-categorical result generalizes for arbitrary Cauchy-complete categories! I'll wait for your proof, since perhaps it directly generalizes to higher categories.
Aug
7
comment Diffeology as a sheaf on the site of smooth manifolds
@Todd: Great, thanks! What I did above, is just show that the set-valued presheaf result implies the infinity-presheaf result, which in particular, implied the groupoid-valued presheaf result that Eugene wanted.
Aug
7
comment Diffeology as a sheaf on the site of smooth manifolds
@Todd: The result about presheaves is a stronger result. Since the Grothendieck topology on $\mathbf{Open}$ is the same as the one induced by restriction from $\mathbf{Man}$, the result about presheaves implies the one about sheaves.
Aug
7
revised Diffeology as a sheaf on the site of smooth manifolds
re-ordered
Aug
7
comment Diffeology as a sheaf on the site of smooth manifolds
OK, I found (and fixed) a small error in the proof. What would be helpful in the future, is constructive feedback however.
Aug
7
revised Diffeology as a sheaf on the site of smooth manifolds
added 458 characters in body
Aug
6
comment Diffeology as a sheaf on the site of smooth manifolds
Could whoever downvoted, please explain to me why? Because if there is math error, I would like to know.
Aug
6
revised Diffeology as a sheaf on the site of smooth manifolds
found a hole in my argument, so gave a new one
Aug
6
awarded  Necromancer