25,860 reputation
576208
bio website
location Münster, Germany
age 28
visits member for 5 years, 8 months
seen Aug 18 at 7:42

I am (... was) 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.

I have written a book about the basics of category theory.

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


Aug
23
awarded  Nice Question
Aug
17
awarded  Revival
Aug
17
comment Residual finiteness: why do we care?
Interesting answer. Judging on the popularity of the different subjects discussed on mathoverflow, we should perhaps rename it as AGflow. (Not to be confused with agflow.com)
Aug
16
comment Can you “combine” Ord and Mon to get Cat?
I doubt that there is such a construction.
Aug
16
comment Ring epimorphisms, and epimorphism in the category of small preadditive cats
There is no restriction of scalars for finitely presented modules.
Aug
16
comment Determining a scheme $X$ is affine from $Qcoh(X)$
Could you please specify your assumptions? Do you mean the following? (a) For every $\Gamma(X,\mathcal{O}_X)$-module $M$ the canonical map $M \to \Gamma(X,\tilde{M})$ is an isomorphism, (b) for every quasi-coherent $\mathcal{O}_X$-module $F$ the canonical map $\widetilde{\Gamma(X,F)} \to F$ is an isomorphism, and (c) for every two quasi-coherent $\mathcal{O}_X$-modules $F,G$ the canonical map $\Gamma(X,F) \otimes \Gamma(X,G) \to \Gamma(X,F \otimes G)$ is an isomorphism?
Aug
16
comment About the functors composition completeness
Usually functors preserving limits are called continuous; they are not called complete. By the way, I think a more natural definition of $Cat_c$ is the $2$-category of complete categories and continuous functors and natural transformations.
Aug
15
comment “set of all irreducible representations of a group”, set-theoretic issues
Why does the question restrict to the Weil group? By the way, I think that such a question has already appeared on MO.
Aug
15
comment Adding inverses to a symmetric monoidal category (Reference?)
Thank you, but I don't understand any of these issues. I work in the symmetric context, so here everything has the form $a^{-1} b$. The symmetry $b a^{-1} \to a^{-1} b$ is induced by the symmetry $ab \to ba$ - what's the problem? In general, the symmetry $(ca)^{-1} bd = a^{-1} b c^{-1} d \to c^{-1} d a^{-1} b = (ac)^{-1} db$ is, by definition, induced by the obvious symmetry $acbd \to cadb$.
Aug
15
revised Adding inverses to a symmetric monoidal category (Reference?)
added 281 characters in body; edited tags; edited title
Aug
14
comment Adding inverses to a symmetric monoidal category (Reference?)
The tensor product of morphisms $(a,b) \to (c,d)$ and $(a',b') \to (c',d')$, represented by $ebc \to ead$, $e'b'c' \to e'a'd'$, is the morphism $(a'a,bb') \to (c'c,dd')$ represented by $ee' \, bb' \, c'c \to (ebc)(e'b'c') \to (ead)(e'a'd') \to ee' \, aa' \, d'd$.
Aug
14
comment Adding inverses to a symmetric monoidal category (Reference?)
The usual Grothendieck group is recovered by looking at discrete categories. The other questions concern the details, and it will take a while to explain all of them. But this is exactly my question: Has this been done somewhere? When I want to use this construction in a paper, it would be nice to have a proper reference.
Aug
14
comment Adding inverses to a symmetric monoidal category (Reference?)
Quillen only wants multiplications with objects of $S$ to be homotopy equivalences. His $S^{-1} S$ construction is therefore quite different.
Aug
14
revised Adding inverses to a symmetric monoidal category (Reference?)
deleted 1 character in body
Aug
14
comment Adding inverses to a symmetric monoidal category (Reference?)
In compact categories objects are assumed to be dualizable; I want them to be invertible.
Aug
14
comment Categorification of the integers
I think that mathoverflow.net/questions/214767 will answer my question.
Aug
14
revised Adding inverses to a symmetric monoidal category (Reference?)
added 49 characters in body
Aug
14
revised Adding inverses to a symmetric monoidal category (Reference?)
added 49 characters in body
Aug
14
asked Adding inverses to a symmetric monoidal category (Reference?)
Aug
12
comment Categorification of the integers
No, $X+1=0$ does not imply $X^2=1$. We are in a rig.