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location Seville, Spain
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visits member for 3 years, 3 months
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I'm a mathematician interested in algebraic topology, category theory, homological algebra, and K-theory.


Apr
15
reviewed Approve suggested edit on Degree and quasi projective family
Apr
15
reviewed Reject suggested edit on nontrivial theorems with trivial proofs
Apr
15
reviewed Reject suggested edit on nontrivial theorems with trivial proofs
Apr
10
comment Definition of a cylinder functor in Waldhausen's K-theory
I think that at least the following is clear (3) => (2) => (1).
Apr
8
comment Projectives and Injectives in Functor Categories
@BugsBunny: Yes, it's also Grothendieck. Projectives are easy, they are just 'tensor products' of representables and projectives in $A$. It's actually the easiest part and doesn't need the strength of Grothendieck categories. As for references, if the target is Ab then probably Freyd's book on abelian categories. Otherwise Ulmer maybe?
Apr
8
comment Projectives and Injectives in Functor Categories
If $A$ were a Grothendieck category the answer would be yes, even under smaller assumptions. I wonder what you have in mind when you require $A$ to have just 'very small' (co)products.
Apr
8
reviewed Approve suggested edit on Inversion of Radon transform by incomplete data: specific case
Apr
8
reviewed Reject suggested edit on Generalized Radon transform (Relaxed sufficient condition for invertibility)
Apr
6
comment Divisible torsion Z-modules
Stated without proof? Have you tried to find the proof in other references?
Apr
6
comment Divisible torsion Z-modules
How do you know it is bijective?
Apr
5
comment Idempotents split in category of smooth manifolds?
Since $p$ is a projection on tangent spaces it can probably be realized (locally) as a standard projection on $\mathbb R^n$. This may lead you to find euclidean neighbourhoods for the image of $p$.
Apr
3
comment Topological degree and polynomial degree
@LiviuNicolaescu and AlexDegtyarev sorry I misread the question and thought he was just talking about homeomorphisms.
Apr
3
comment Topological degree and polynomial degree
@AlexDegtyarev it can be defined as the value of the automorphism induced on $2n$-dimensional cohomology with compact support (or homology with infinity support). In that dimension the aforementioned cohomology is $\mathbb Z$.
Apr
3
comment Making additive envelopes of monoidal categories monoidal
Indeed, I mean enriched in abelian groups.
Apr
3
comment Making additive envelopes of monoidal categories monoidal
I've corrected that tag. I guess you should add that $\mathcal C$ is additive. Your construction looks correct to me, but I don't know of any reference.
Apr
3
revised Making additive envelopes of monoidal categories monoidal
edited tags
Apr
3
answered Universal coefficient theorem for local ring
Apr
2
comment Split exact categories arising naturally
Isn't it true that any karoubian split exact category is equivalent to the category of projective modules over a ring?
Mar
31
comment Why should noncommutative CYs be dgas?
@Steve you shouldn't look at ordinary algebras as opposed to dgas, you should rather look at the former contained in the latter. The coordinate ring of a variety $X$ must be understood as a dga $A$ such that $D^b(X)\simeq D(A)$. Of course $A$ is in generaly only defined up to derived Morita equivalence. If $X$ is an affine variety, $A$ is the classical coordinate ring. But for many varieties you need an honest dga (think of projective varieties).
Mar
29
reviewed Reject suggested edit on algebraic-k-theory tag wiki