23,603 reputation
464177
bio website wwwmath.uni-muenster.de/u/…
location Münster, Germany
age 27
visits member for 4 years, 9 months
seen 57 mins ago

I am interested in the interactions between algebraic geometry and category theory. More specifically, I "model" algebraic geometry on cocomplete symmetric monoidal categories.

Here is a link to my PhD thesis. Comments are welcome.

Email: [my last name] [at] uni-muenster.de


Sep
15
awarded  Popular Question
Sep
13
comment When does sheaf cohomology commute with arbitrary direct sums?
Direct sums are filtered colimits of finite direct sums. And finite direct sums are no problem.
Sep
10
comment Canonical presentation of pro-modules over pro-rings
The maps $M_{j+1} \to M_i$ are surjective. It follows easily that each projection $\widehat{M} \to M_j$ is surjective (construct inverse images recursively). Hence, also $\alpha_j$ is surjective.
Sep
10
comment Canonical presentation of pro-modules over pro-rings
From $K_{ji} = M_{j+i} I_{ij}$ for all $i$ we only get $\widehat{K_j} = \varprojlim_i \, (M_{j+i} \cdot I_{ji})$, but why does this equal $\varprojlim_i \, M_{j+i} \cdot \varprojlim_i \, I_{ji} = \widehat{M} \widehat{I_j}$? Again, $\subseteq$ is unclear.
Sep
10
comment Canonical presentation of pro-modules over pro-rings
Thank you. But $\widehat{K_j} = \widehat{I_j} \widehat{M}$ is unclear to me (and clearly this is a direct reformulation of the claim). How do you prove $\subseteq$?
Sep
8
comment Canonical presentation of pro-modules over pro-rings
Sure, the isomorphisms belong to the data. A morphism $M \to N$ is a family of morphisms $M_i \to N_i$ compatible with the isomorphisms. Actually all this follows from the definition $\mathcal{M} := \varprojlim_i \, \mathsf{Mod}(A_i)$.
Sep
8
asked Canonical presentation of pro-modules over pro-rings
Aug
30
comment A short proof for $\dim(R[T])=\dim(R)+1$
R. Gilmer is the author, but of which paper?
Aug
17
awarded  Popular Question
Aug
14
comment Coherent sheaves and Mitchell's embedding theorem
Some comments. a) The embedding theorem doesn't work (a priori) for all abelian categories - we need essentially small abelian categories. I suggest to look at the category of quasi-coherent sheaves of finite type (resp. of finite presentation) since that is essentially small. b) "coherent" is something stronger than "finitely generated" (although Hartshorne's book suggests this). c) Even for $\mathbb{P}^1_k$ the question is not easy to answer, I think, even though one understands the quasi-coherent sheaves very well here.
Aug
14
comment Pursuing an abelian categorical proof of the Zassenhaus Lemma
You may use the embedding theorem. The reason is that the embedding is fully faithful and exact. So it preserves intersections and sums of subobjects, and it reflects isomorphisms (basically everything you need).
Aug
14
comment symmetric monoidal dagger endofunctor categories
@DavidWhite: Day convolution needs colimits with distribute over the tensor product.
Aug
14
comment Existence of Colimits in the Definition of Locally Presentable Categories
@ZhenLin: What about making this an answer?
Aug
4
comment A short proof for $\dim(R[T])=\dim(R)+1$
@NeilStrickland: The following example can be found in Hutchins, Examples of Commutative Rings, Example 27: Let $k$ be a field and let $R = k(y)[[x]] \times_{k(y)} k$ the ring of those power series in $x$ with coefficients in $k(y)$ resp. $k$ for the constant term. Then $\dim(R)=1$ and $\dim(R[T])=3$. I've also read that actually every number between $\dim(R)+1$ and $2 \dim(R)+1$ may appear as $\dim(R[T])$.
Jul
26
asked Open covering of the Hilbert functor of points
Jul
23
comment Infinite Tensor Products
@ashpool: $U=K^x$, which is trivial when $K=\mathbb{F}_2$.
Jul
21
awarded  Enlightened
Jul
21
awarded  Nice Answer
Jul
17
comment Tensor product of pullbacks of abelian categories
Sorry but this doesn't help me. I doubt that universal properties will help (we interchange colimits with limits). Also it's unclear to me what is nice here. The transfinite recursion in the reflection is horrible.
Jul
8
asked Tensor product of pullbacks of abelian categories