bio  website  wwwmath.unimuenster.de/u/… 

location  Münster, Germany  
age  27  
visits  member for  4 years, 9 months 
seen  33 mins ago  
stats  profile views  34,483 
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] unimuenster.de
14h

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 15 
comment 
A short proof for $\dim(R[T])=\dim(R)+1$
I've read the proof. It is basically the usually one, cites ZariskiSamuel for a result which depends on Krull's Principal Ideal Theorem. My question was not about some proof (which can be found in almost every commutative algebra text), but rather about a very specific proof, using the characterization by T. Coquand and H. Lombardi. => 1 
Oct 14 
comment 
Classification of rings satisfying $a^4=a$
A counterexample is given in ArensKaplansky, "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 $a^4=a$
ArensKaplansky couldn't use the language of functors etc., but what they did is to show that the functor from the algebraic side to the geometric side is fully faithful. They didn't do anything in the other direction, and also didn't prove a duality result. This could be new (... until I finally find a paper where this has been done?). 
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 $[\mathbb{A}^n / \mathrm{GL}_n]$ 
Oct 13 
awarded  Nice Question 
Oct 13 
accepted  Concise definition of subobjects 
Oct 13 
comment 
The quotient stack $[\mathbb{A}^n / \mathrm{GL}_n]$
Yes. What is the stabilizer group scheme of the nonzero point? 
Oct 13 
comment 
Classification of rings satisfying $a^4=a$
I am still not convinced. I don't see any embedding without using some actions. If Neil's answer is correct (which I believe more and more), then the classification in terms of closed subsets would mean, roughly, that any $C_2$action on a Stone spaces splits outside the closed subset of fixed points, where I call a $C_2$space split iff it is isomorphic to $Y \coprod \sigma Y$ for some space $Y$. I don't see any reason why there should be such a splitting. And this is also where cohomology might show obstructions. 
Oct 13 
answered  Classification of rings satisfying $a^4=a$ 
Oct 13 
comment 
Classification of rings satisfying $a^4=a$
I think I have found a proof that $R \to F(G(R))$ is an isomorphism, but it's quite long. Should I make this a CW answer? 