bio  website  personal.us.es/fmuro 

location  Seville, Spain  
age  
visits  member for  3 years, 8 months 
seen  26 mins ago  
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I'm a mathematician interested in algebraic topology, category theory, homological algebra, and Ktheory.
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

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Golod Shafarevich Inequality and Inequalities among higher Cohomology groups
What does inequality between abelian groups mean? 
Sep 17 
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Perf($\mathscr{A}$) and perfect chain complexes
It's obvious, at least to me. What's the part you don't see? 
Sep 16 
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Construction of generalized EilenbergMacLane 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 
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Getting a Postnikov Tower from the Tottower?
The Postnikov tower is not always a tower or principal fibrations. I have the feeling that the tottower 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 
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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 
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What is a stable $(n,1)$category?
@QiaochuYuan $\pi_0$ of a stable inftycategory is triangulated. Anyway, all this is speculation. 
Sep 12 
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What is a stable $(n,1)$category?
Picard groupoids form an abelian 2category 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 inftycategories enhance. 
Sep 11 
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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 nonclosed example in mind? 
Sep 11 
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Higher coherent multiplicative structures on Salgebras
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 
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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 
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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 BCduals 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 BCduals 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 
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Zigzags and contractibility of categories
I think Omar is right. You seem to be describing the GabrielZisman 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=4g4 when genus $\ge 1$ 