bio  website  personal.us.es/fmuro 

location  Seville, Spain  
age  
visits  member for  4 years, 5 months 
seen  1 hour ago  
stats  profile views  5,832 
I'm a mathematician interested in algebraic topology, category theory, homological algebra, and Ktheory.
2d

comment 
$\pi_8(S^5)=\pi_8(SO(6))=\mathbb{Z}/24$?
en.m.wikipedia.org/wiki/Jhomomorphism 
2d

comment 
Convergence of the Lyndon  Hochschild  Serre spectral sequence
For me Boardman's paper was very helpful since it analyzes different notions of convergence and I learnt them by comparing, that's why I recommend it. 
2d

comment 
Convergence of the Lyndon  Hochschild  Serre spectral sequence
No, I would recommend you the following paper by Boardman, where everything is very well explained hopf.math.purdue.edu/Boardman/ccspseq.pdf 
Jul 1 
comment 
Does projective imply flat?
@TheoJohnsonFreyd the argument I had in mind wrongly assumed that $\hom(,I)$ had to be exact, where $\hom$ is the inner $\hom$ and $I$ is an injective object. But asking that is no different to asking projectives to be flat. Sorry for creating wrong expectations ;) 
Jun 30 
comment 
Does projective imply flat?
If you have enough injectives, then yes, would you be willing to assume this? 
Jun 26 
comment 
Whitehead group
Listing all classes that do and all classes that don't, apart from ambiguous, it seems to me like asking too much. 
Jun 22 
comment 
Pretriangulated category that isn't triangulated
@Bobson I'm sceptical about this question being settled very quickly. I'd favour a counterexample, but it must be a difficult one and I don't think there's many people thinking of these things. 
Jun 19 
comment 
Homotopy type of a CW complex
Yes mathoverflow.net/questions/156266/… 
Jun 18 
comment 
Pretriangulated category that isn't triangulated
@DylanWilson yes, it seems that there's still some work to be done in order to elucidate the answer. It's very laudable that Antony Maciocia has tried so hard, this might encourage some other people to look for another proof or a counterexample. Maybe you could unmark this answer in order to keep the question alive? (It's not that I want less points for Bobson ;) ) 
Jun 18 
reviewed  Approve Chopping up Dynkin diagrams 
Jun 18 
comment 
Higher refinement of Seifertvan Kampen theorem on the language of hocolim
I totally agree with @EricWofsey Morally, the fundamental infinity groupoid is the space itself, so you find the same thing at both sides of the equation. Brown's version need not be for filtered spaces, I mean, the skeletal filtration is fine and canonical. I'd say that such a result really represents a simplification when you replace $\Pi_1$ with something which is easy enough, such that the fundamental crossed module, categorical group, etc. 
Jun 17 
comment 
Definitions of the module $R/(x_0^\infty,x_1^\infty,\ldots,x_{n1}^\infty)$
The first construction is problematic if $x_0,\dots, x_k$ is not a regular sequence. 
Jun 16 
comment 
Need M combinatorial for existence of injective model structure on $M^G$?
Mike, concerning your last paragraph, you probably have seen these: Reedy model structures on diagrams indexed by an inverse category. 
Jun 14 
revised 
$\Omega X$action on spectral $X$bundles
added 25 characters in body 
Jun 10 
reviewed  Approve configuration space and iterated loop space 
Jun 3 
comment 
What are algebras for the little nballs/ncubes/nsomething operads exactly?
3 no's :) I don't have a proper computer at hand now, otherwise I could contribute to the debate that will probably start now. Maybe later. 
Jun 3 
reviewed  Approve An inequality for eigenvalues of the Dirichlet problem 
Jun 3 
comment 
Pretriangulated category that isn't triangulated
I think it's a great, major achievement! 
Jun 2 
awarded  Nice Answer 
Jun 1 
answered  Solving algebraic problems with topology 