bio  website  math.berkeley.edu/~qchu 

location  Berkeley, CA  
age  24  
visits  member for  5 years, 6 months 
seen  4 hours ago  
stats  profile views  59,829 
I am a thirdyear graduate student at UC Berkeley. I'm interested in the interplay between homotopy theory, quantum field theory, manifold topology, and higher category theory.
15h

awarded  Nice Answer 
Apr 17 
awarded  Notable Question 
Apr 13 
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Maps to the group completion
Surely being an Hspace isn't a sufficient condition to admit a delooping? 
Apr 13 
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klinear abelian categories which are not categories of modules
On the other hand, that does suggest how to adapt the above construction to $B'$. We take the subalgebra of $B'$ consisting of sequences $a_i \in M_i(\mathbb{F}_2)$ such that $a_i$ is eventually a scalar and $\lim_{i \to \infty} a_i = a_1$. That might work. But it can be ruled out by removing $M_1(\mathbb{F}_2)$ from the product... and to rule out similarlooking constructions let's maybe only take the product over prime $i$. 
Apr 13 
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klinear abelian categories which are not categories of modules
@Eric: that does not work for $B$. The subalgebra $A$ you suggest is the subalgebra of sequences $a_i \in \mathbb{F}_2$ such that $\lim_{i \to \infty} a_i$ exists, and as such it has an extra map $A \to \mathbb{F}_2$ not factoring through the distinguished finite quotients of $B$, namely $\lim_{i \to \infty} a_i$ itself. The induced map $A \to B$ of Boolean rings corresponds topologically to the natural map from the StoneCech compactification of $\mathbb{N}$ to its onepoint compactification. 
Apr 13 
revised 
klinear abelian categories which are not categories of modules
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Apr 13 
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klinear abelian categories which are not categories of modules
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Apr 13 
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klinear abelian categories which are not categories of modules
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Apr 13 
answered  klinear abelian categories which are not categories of modules 
Apr 13 
awarded  Announcer 
Apr 13 
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klinear abelian categories which are not categories of modules
Also, in the question, by "equivalent" do you just mean as $k$linear categories or do you mean as $k$linear categories together with a choice of fiber functor? 
Apr 13 
awarded  Enlightened 
Apr 13 
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klinear abelian categories which are not categories of modules
The result you cite (with "comodule" replaced by "finitedimensional comodule") requires crucially the hypothesis that $C$ is essentially small, or else the endomorphism algebra of $U$ can fail to be a set. For an explicit counterexample, take the category of finitedimensional $\text{Ord}$graded vector spaces. $\text{End}(U)$ has an idempotent for each ordinal given by projecting to the subspace indexed by the corresponding ordinal. 
Apr 9 
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How do I apply the Boolean Prime Ideal Theorem?
@Manny: that is a proof that the method ultimately won't work, but it's not an explanation of why I can't immediately adapt this method to prove the corresponding statement for maximal rather than prime ideals. 
Apr 9 
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How do I apply the Boolean Prime Ideal Theorem?
So I guess the reason this method will not work to prove the corresponding statement for maximal rather than prime ideals is that maximality is not expressible in the firstorder language of rings? 
Apr 9 
awarded  homotopytheory 
Apr 9 
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What's the cardinality of a higher category?
@Simon: yes, of course I want the obvious finiteness conditions. I would hesitate to call this number "Euler characteristic," though; to my mind the Euler characteristic is set up to have nice behavior with respect to cofiber sequences rather than fiber sequences. 
Apr 9 
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Is the infinitygroupoid of a finite CW complex finitelypresented?
Another way to say it: a presentation of a group is a description of that group as the cokernel of a map between free groups. Keeping in mind the analogy to free resolutions of modules, we might say more generally that "presentation" means "description of an object as a colimit of free objects." And a CW decomposition is precisely a description of a space as an iterated homotopy pushout of spheres (which themselves are iterated homotopy pushouts of points). 
Apr 9 
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Is the infinitygroupoid of a finite CW complex finitelypresented?
...new "generators" in the sense that they may (before we kill them again) give rise to higher homotopy and new "relations" in the sense that they themselves kill homotopy. 
Apr 9 
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Is the infinitygroupoid of a finite CW complex finitelypresented?
This is a modelindependent statement. Of course it depends on what the OP means by "free $\infty$groupoid on a finite family of generators," but I think this is a reasonable interpretation. Think first about how one presents a group $G$ in terms of generators and relations. Topologically generators correspond to $1$cells and relations correspond to $2$cells. So in fact a presentation describes a CW complex of dimension $2$ (the presentation complex). This is the beginning of a presentation / CW description of $BG$, and one now needs to add $3$cells, etc. These are simultaneously... 