24,153 reputation
567187
bio website wwwmath.uni-muenster.de/u/…
location Münster, Germany
age 27
visits member for 4 years, 11 months
seen 1 hour 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


Nov
18
answered Why are flat morphisms “flat?”
Nov
18
comment an easy example of valuation ring which is not noetherian?
Yes. en.wikipedia.org/wiki/…
Nov
17
awarded  Nice Answer
Nov
8
awarded  Good Question
Nov
3
comment Sexy vacuity …
A consequence of $\sup(\emptyset)=-\infty$ is that the Krull dimension of the zero ring is $-\infty$. Notice that this is consistent with $\dim(R \times S)=\max(\dim(R),\dim(S))$. Usually rings in which prime ideals are maximal are called zero-dimensional, but this is not quite true: The zero ring is not zero-dimensional, but still every prime ideal is maximal (vacuously).
Nov
3
comment Sexy vacuity …
@KevinBuzzard: Defining $|f|$ as the smallest real number such that $f$ maps balls with radius $r$ into balls with radius $|f|r$, for all $r > 0$, should work for all cases, right?
Oct
21
awarded  Good Question
Oct
21
awarded  Popular Question
Oct
19
comment Sexy vacuity …
@AndreasBlass: Wow, this is a very concise definition! We could also say that on a connected space every continuous function should be constant of some value (i.e. factors over $\{\star\}$). But functions on $\emptyset$ have no value.
Oct
16
comment Examples of common false beliefs in mathematics
@Michael: $\mathbb{Z} \subseteq \mathbb{Q}$
Oct
16
revised Examples of common false beliefs in mathematics
added 10 characters in body
Oct
16
awarded  Popular Question
Oct
15
revised A short proof for $\dim(R[T])=\dim(R)+1$
added 247 characters in body
Oct
14
comment Classification of rings satisfying $a^4=a$
A counterexample is given in Arens-Kaplansky, "Topological representations of algebras", Section 8.
Oct
14
comment Classification of rings satisfying $a^4=a$
Meanwhile I have also found a proof for $X \cong G(F(X))$.
Oct
14
comment Classification of rings satisfying $a^4=a$
I am very stupid, or at least forgetful. In the paper "Topological representation of algebras" (1947), which I already read several years ago, Arens and Kaplansky give exactly this classification of $4$-rings in terms of $C_2$-actions. And the proof is very simple, one just extends scalars to $\mathbb{F}_4$, where classification is simple, and then one does (what is nowadays called) descent.
Oct
14
comment Theme of Isbell duality
I've read that objects which belong to two concrete categories at once are called schizophrenic. Usually schizophrenic objects induce adjunctions.
Oct
14
accepted Classification of rings satisfying $a^4=a$
Oct
14
comment The quotient stack $[\mathbb{A}^n / \mathrm{GL}_n]$
Thank you for adding the picture.
Oct
14
accepted The quotient stack $[\mathbb{A}^n / \mathrm{GL}_n]$