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bio website personal.us.es/fmuro
location Seville, Spain
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visits member for 3 years, 8 months
seen 26 mins ago

I'm a mathematician interested in algebraic topology, category theory, homological algebra, and K-theory.


2d
reviewed Approve suggested edit on What are all positive integers n for which the congruence $a^{n+1} \equiv a (mod n)$ holds?
2d
comment Golod Shafarevich Inequality and Inequalities among higher Cohomology groups
What does inequality between abelian groups mean?
Sep
17
comment Perf($\mathscr{A}$) and perfect chain complexes
It's obvious, at least to me. What's the part you don't see?
Sep
16
comment Construction of generalized Eilenberg-MacLane spaces
I'd recommend Baues' obstruction theory book.
Sep
16
reviewed Approve suggested edit on Concentration results for inner products of two independent random gaussian vectors
Sep
16
reviewed Approve suggested edit on Vanishing homology of simplicial complexes with few facets
Sep
16
reviewed Approve suggested edit on Weighted graph similarity
Sep
14
comment Getting a Postnikov Tower from the Tot-tower?
The Postnikov tower is not always a tower or principal fibrations. I have the feeling that the tot-tower is (because it is associated to simplicial skeleta, whose inclusions are principal cofibrations). Hence the answer to your question might be 'no'. But I'm just speculating with this. I didn't check anything.
Sep
13
comment What is a stable $(n,1)$-category?
BTW, let me mention, in case you find it interesting, that there is a purely algebraic notion of $2$-ring whose modules form an abelian $2$-category. These $2$-rings model ring spectra with htpy groups concentrated in degree $0$ and $1$. They represent classes in third MacLane cohomology.
Sep
13
comment What is a stable $(n,1)$-category?
@QiaochuYuan $\pi_0$ of a stable infty-category is triangulated. Anyway, all this is speculation.
Sep
12
comment What is a stable $(n,1)$-category?
Picard groupoids form an abelian 2-category in the sense of Pirashvili, Vitale & co. However I don't quite agree with you taking abelian categories for $n=1$. I'd take triangulated categories, which is what stable infty-categories enhance.
Sep
11
comment Category of modules over commutative monoid in symmetric monoidal category
I don't even see how can one check associativity of $\otimes_A$ if $\otimes$ doesn't preserve colimits, which is automatic in the closed case, of course. Maybe you can do it with weaker hypothesis but, do you really have a non-closed example in mind?
Sep
11
comment Higher coherent multiplicative structures on S-algebras
Modules over an algebra over an operad have a model structure. You can then try to put a tensor product compatible with the model structure on $A$-modules. It seems sensible, but I don't know of any reference.
Sep
9
awarded  Enlightened
Sep
5
comment Latching space functor in Reedy model strucutre
The latching object at $1$ is the initial object, not $A$, it seems to me.
Aug
28
reviewed Approve suggested edit on Stable analytic manifold under simple action
Aug
18
comment pontryagin dual and maps between spectra
The answer to your question is obviously yes, since any abelian group arises as the group of homotopy classes of maps between certain spectra. If you want BC-duals to show up, your abelian group is $\pi_0I_{\mathbb{Q}/\mathbb{Z}}F(A,B)$, where $F(A,B)$ is the function spectrum. If you want to use the BC-duals of $A$ and $B$, you should first try to anser your question for ordinaryt abelian groups instead of spectra.
Aug
14
answered Zigzags and contractibility of categories
Aug
13
comment Zigzags and contractibility of categories
I think Omar is right. You seem to be describing the Gabriel-Zisman localization of $\bf C$ at all arrows, i.e. the groupoidification of $\bf C$. Hence $Z\bf C$ is the fundamental groupoid of the nerve of $\bf C$, and it has an initial object iff it is trivial, but this says nothing about the higher homotopy groups of $\bf C$, unfortunately.
Aug
13
reviewed Approve suggested edit on simple explanation of simplicial volume=4g-4 when genus $\ge 1$