338 reputation
16
bio website
location Northwestern University
age 23
visits member for 1 year, 11 months
seen Sep 4 at 3:35
I'm a first-year grad student at Northwestern. I like homotopy theory and that thing where you stand across the street from people in a parka and yell at them.

Feb
21
asked Failure of Noether normalization
Oct
11
awarded  Yearling
Jun
25
awarded  Custodian
Jun
25
reviewed Reviewed Homological Algebra texts
Jun
10
comment Explanations for mathematicians, about the falsifiability (or not) of string theory
@JHI en.wikipedia.org/wiki/Falsifiability
May
19
comment Composition in the category quotient
$g$ is a map $N'' \to P/P'$; taking a further quotient induces $N'' \to P/P''$; and then by definition, $N' \cap N''$ is a subobject of the kernel of this map, so it passes to $N''/(N'\cap N'')\to P/P''$. There's a good reason why arguments about abelian categories look like arguments about modules: the Freyd-Mitchell embedding theorem, which says that any small abelian category embeds into some category of modules over a ring. So any statement you can phrase in terms of an arbitrary small set of objects in an abelian category, and prove when those objects are modules, is true in general!
May
18
answered Composition in the category quotient
May
16
comment Computation of Ext(Z^N,Z)
This should answer your question: mathoverflow.net/questions/40499/…
May
6
answered Definition of subobject classifier in presheaves
May
3
comment Split and pure exact sequence of sheaves
Tensor products commute with direct sums, and if the sequence is split, $B \cong A \oplus C$.
Apr
28
comment Is there a local projective model structure on simplicial sheaves? What are its fibrant objects?
This paper (math.uiuc.edu/K-theory/0462/combination2.pdf) by Benjamin Blander seems to imply that the answer to your first question is 'yes,' and you again get a Quillen equivalent model category, with sheafifying and forgetting being a Quillen equivalence.
Mar
22
comment Intuition as to why the K-theory of a ring should be the homotopy theory of an H-space
That isn't really an answer to your questions, so for now let me just make an insinuation: what could you mean by a space 'naturally' having a multiplication on its homotopy groups, other than this being induced by a multiplication on the space itself?
Mar
22
comment Intuition as to why the K-theory of a ring should be the homotopy theory of an H-space
In fact the $K$-groups of a ring are naturally modelled as the homotopy groups of a spectrum. (If you want to stick with spaces, you can in turn model this as an infinite loop space, i.e. a space which can be expressed as the form $\Omega^nX_n$ for some space $X_n$, for every $n$.) When you're starting with a ring, the spectrum you get is always a ring spectrum, which is the spectrum version of an $H$-space. I don't actually know why this is true, but I'd guess it pops out of one of the various constructions of this spectrum.
Mar
4
awarded  Teacher
Mar
4
answered injectivity is a local property over noetherian rings
Mar
4
comment $\pi$-cohomology class — a variant of cohomology class
In order for this to be well-defined, you'd need to say precisely what it means for two cycles to '"deform" into each other continuously.' If both cycles are subcomplexes of $X$, you could ask for them to be simplicially homotopic, but then you'd want your simplicial set to be Kan, i. e. probably the singular complex of the space $X$ rather than a triangulation. Then you'd need to make sure that your definition extends well to the abelian group of cycles.
Feb
27
awarded  Critic
Nov
19
awarded  Supporter
Nov
9
awarded  Nice Question
Nov
9
awarded  Student