7,138 reputation
1540
bio website people.mpim-bonn.mpg.de/…
location Bonn
age 32
visits member for 4 years, 9 months
seen 18 hours ago

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.


Dec
15
comment Characterizing local homeomorphisms into an exponent
OK, fair enough. I follow the category-theorist convention of only writing $X^Y$ for a genuine internal-hom, that is, something satisfying the correct universal property, but at any rate, there is no risk of confusion in my question, since I restrict to compactly generated spaces, which are Cartesian-closed.
Dec
12
comment Characterizing local homeomorphisms into an exponent
I need $Y^X$ to exist, so I was restricting to a Cartesian closed subcategory. in $Top$, this is only possible if $X$ is core-compact.
Dec
9
comment Morphism on schemes induced by continuous morphism of sites
@ZhenLin: I agree.
Dec
9
comment Morphism on schemes induced by continuous morphism of sites
Apparently I did. I misread the statement of the theorem, and have updated to correct for this.
Dec
9
revised Morphism on schemes induced by continuous morphism of sites
addressed structure sheaves
Dec
9
comment Morphism on schemes induced by continuous morphism of sites
@ZhenLin: Ah ha! Mystery solved.
Dec
9
comment Morphism on schemes induced by continuous morphism of sites
@ZhenLin, how does this tie in with your counterexample?
Dec
9
comment Morphism on schemes induced by continuous morphism of sites
@user46578: See this paper of Pronk: eudml.org/doc/90454. Apparently you do not have carry along the structure sheaf.
Dec
9
answered Morphism on schemes induced by continuous morphism of sites
Nov
30
comment When do zero-simplices of a simplicial diagram determine its homotopy colimit?
@DmitriPavlov: I'm not asking for what $\mathscr{C}$ is this true for all $X_\bullet$. I'm asking, given $\mathscr{C}$, for what $X_\bullet$ is this true.
Nov
28
revised When do zero-simplices of a simplicial diagram determine its homotopy colimit?
added 28 characters in body
Nov
28
answered When do zero-simplices of a simplicial diagram determine its homotopy colimit?
Nov
28
answered When do zero-simplices of a simplicial diagram determine its homotopy colimit?
Nov
28
revised When do zero-simplices of a simplicial diagram determine its homotopy colimit?
added 18 characters in body
Nov
28
asked When do zero-simplices of a simplicial diagram determine its homotopy colimit?
Nov
27
comment Site dependance of the Cech weak equivalences on simplicial sheaves
Don't you mean finite limits above, not finite products?
Nov
27
comment Site dependance of the Cech weak equivalences on simplicial sheaves
I learned this from Jacob Lurie: Let $Q=\prod_i I$ be the hilbert cube. Consider all the open subsets which are homeomorphic to $Q \times [0,1)$. These form a basis, but are not closed under finite intersections. Considering them as a subcategory of the poset of all open subsets, one can define an obvious site structure. However, infinity sheaves on this site is different than infinity sheaves on the Hilbert cube.
Nov
27
comment Site dependance of the Cech weak equivalences on simplicial sheaves
There has to be, since assuming there is no counterexample, one could show that both sites yield the same infinity-topos.
Nov
27
answered Site dependance of the Cech weak equivalences on simplicial sheaves
Nov
23
accepted When is a topological space the homotopy colimit of an open covering?