bio | website | |
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location | Münster, Germany | |
age | 28 | |
visits | member for | 5 years, 8 months |
seen | Aug 18 at 7:42 | |
stats | profile views | 38,321 |
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 |
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Ring epimorphisms, and epimorphism in the category of small preadditive cats
There is no restriction of scalars for finitely presented modules. |
Aug
16 |
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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 |
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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 |
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“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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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Categorification of the integers
No, $X+1=0$ does not imply $X^2=1$. We are in a rig. |