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location Seville, Spain
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visits member for 4 years, 6 months
seen 1 hour ago

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


2h
comment Explicit structure of certain $E_\infty$ generalization of the Artin algebras $k[\epsilon]/\epsilon^2$ and their inverse limit
Could you include references of those papers were that concept is mentioned? I understand that without definition or reference to where they are defined.
1d
comment A tensor product for triangulated categories?
Sure, it's a very interesting question. One can learn a lot even from a counterexample. It might be easier to show that the tensor product of triangulated categories does not carry a triangulation, but the non-existence of a canonical triangulated envelop could be much more difficult.
1d
comment A tensor product for triangulated categories?
I think it's unlikely. Wouldn't this mean that you can recover the derived category of $H\mathbb F_p\wedge H\mathbb F_p$ out of the category of $\mathbb F_p$-vector spaces? A possible way towards a counterexample would be taking a triangulated category with two models $C$ and $D$ and trying to check that the homotopy categories of the tensor squares $C\otimes C$ and $D\otimes D$ are different, but I don't have any simple example in mind to carry out this.
Jul
27
comment Is there a generalization of homotopy groups to fractional dimensions
Rationals are overrated.
Jul
24
comment divisible 2nd cohomolgy group $H^2(G,\mathbb{Z}G)$
@ThiKu your M must be aspherical.
Jul
15
comment Homological vs. cohomological dimension of a group/space
In don't understand this argument. What's the projective/flat dimension of a complex? How can Tor be non-trivial if the second argument is projective?
Jul
15
comment Homological vs. cohomological dimension of a group/space
This actually answers Q3 not only for $X=BG$ but for any $X$ since the canonical map $X\rightarrow B\pi_1(X)$ induces an isomorphism on $H^1$ with coefficients in any $\pi_1(X)$-module.
Jul
15
revised Homological vs. cohomological dimension of a group/space
added 49 characters in body
Jul
14
comment Homological vs. cohomological dimension of a group/space
Sorry, it seems that when answering Q3 I suddenly forgot that we're considering local coefficients.
Jul
14
revised Homological vs. cohomological dimension of a group/space
added 55 characters in body
Jul
13
answered Homological vs. cohomological dimension of a group/space
Jul
5
comment Does the stable category of a nice exact category embed in (the underlying category of) a derivator?
I would check with Cisinski's paper whether the axioms of a derivable category holds. I don't have it at hand now.
Jul
3
comment $\pi_8(S^5)=\pi_8(SO(6))=\mathbb{Z}/24$?
en.m.wikipedia.org/wiki/J-homomorphism
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
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.