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442126
bio website math.berkeley.edu/~amathew
location Berkeley, CA
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visits member for 5 years, 3 months
seen 8 hours ago

Graduate student at UC Berkeley.


Jan
26
accepted Can any object in a presentable category be written as a colimit of generators?
Jan
26
comment Can any object in a presentable category be written as a colimit of generators?
Todd and @MikeShulman, thanks for explaining this.
Jan
26
comment Can any object in a presentable category be written as a colimit of generators?
Interesting. Could you (or Mike) perhaps elaborate why $\mathbb{2}$ is not a colimit-dense generator in $Cat$?
Jan
26
revised Can any object in a presentable category be written as a colimit of generators?
added 480 characters in body; edited title
Jan
26
asked Can any object in a presentable category be written as a colimit of generators?
Jan
24
awarded  Necromancer
Jan
23
awarded  Revival
Jan
23
answered What is to tmf as KR is to KO?
Jan
14
awarded  Popular Question
Dec
1
comment Is homology finitely generated as an algebra?
@BenWieland: A proof is now in Proposition 8.9 of arxiv.org/pdf/1406.4947v3.pdf
Nov
28
revised Failure of “equivariant triangulation” for finite complexes equipped with a $G$-action
added 2073 characters in body
Nov
28
comment Failure of “equivariant triangulation” for finite complexes equipped with a $G$-action
For $\mathbb{Z}/p$-actions on finite spectra, then if a spectrum $X \in \mathrm{Fun}(B\mathbb{Z}/p, \mathrm{Sp})$ belongs to the thick subcategory generated by $S^0$ and $(\mathbb{Z}/p)_+$, its Tate construction needs to be the $p$-adic completion of a finite spectrum. I was hoping that it might be possible to argue along those lines.
Nov
28
comment Failure of “equivariant triangulation” for finite complexes equipped with a $G$-action
@Jacob: Yes, that's precisely the kind of reasoning that I had hoped would be applicable. I'm also interested in the case of finite group actions on finite spectra (in which case one could hope to use the Segal conjecture). Still, it doesn't seem easy to build a natural example (especially since one would need to be able to say something about the homotopy fixed points for this).
Nov
28
comment Failure of “equivariant triangulation” for finite complexes equipped with a $G$-action
@JacobLurie: I agree, but I'm looking for objects in $\mathrm{Fun}(BG, \mathcal{S})$ whose image in $\mathcal{S}$ is compact; they don't have to be compact in $\mathrm{Fun}(BG, \mathcal{S})$ itself.
Nov
28
asked Failure of “equivariant triangulation” for finite complexes equipped with a $G$-action
Oct
31
awarded  Nice Question
Oct
31
comment Chiral categories versus braided monoidal categories
@DavidBen-Zvi: Sounds like the statement I was looking for. I'll ask Sam about this further when I next see him. Thanks.
Oct
31
comment Chiral categories versus braided monoidal categories
Actually, it looks like you're indicating it does apply in the geometric Satake setting -- so I suppose what I'm looking for is a description (or reference for) the version of Riemann-Hilbert that applies here.
Oct
31
comment Chiral categories versus braided monoidal categories
In particular, I'd be curious if it applies in the geometric Satake setting as well (though I'd also like to understand the E_2-structure in the affine Kac-Moody case).
Oct
31
comment Chiral categories versus braided monoidal categories
@DavidBen-Zvi: Could you elaborate on the condition of "integrability" which enables one to obtain the E_2-category?