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bio website personal.us.es/fmuro
location Seville, Spain
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visits member for 4 years, 5 months
seen 1 hour ago

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


2d
comment $\pi_8(S^5)=\pi_8(SO(6))=\mathbb{Z}/24$?
en.m.wikipedia.org/wiki/J-homomorphism
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?
@TheoJohnson-Freyd 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 Pre-triangulated 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 Pre-triangulated 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 Seifert-van 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 $R/(x_0^\infty,x_1^\infty,\ldots,x_{n-1}^\infty)$
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 n-balls/n-cubes/n-something 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 Pre-triangulated 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