45,125 reputation
13168421
bio website math.berkeley.edu/~qchu
location Berkeley, CA
age 24
visits member for 5 years, 2 months
seen 42 mins ago

I am a third-year graduate student at UC Berkeley. I'm interested in the interplay between homotopy theory, quantum field theory, manifold topology, and higher category theory.


6h
comment What is a totient?
@Joonas: so "totient function" means a function counting the number of times something happens?
6h
comment What is a totient?
I think the question is why such a general definition deserves the name "totient." Is it just by analogy with the Euler totient function or is there some general non-mathematical meaning of the word "totient" that is being invoked here?
1d
comment Cantor's theorem for presheaves?
@Michal: this is obvious if you require that $C$ is small. I think Todd wants to take $C$ to be $U$-small relative to a universe $U$ and then I guess things are okay if $\text{Set}$ is also the $U$-small version? I'm not very familiar with exactly what operations are and aren't allowed when working with universes, and in particular I don't know anything about forming $U$-small functor categories.
1d
comment Cantor's theorem for presheaves?
@Theo: I think there are at least two problems with that argument, one being that at best you'll prove the statement with "essentially surjective" replaced by "surjective," but the other being that that to get a cartesian closed category of categories we need to restrict our attention to small categories, but then we disallow $\text{Set}$ itself...
1d
comment What's so special about $1$-categories?
@Fernando: my understanding is that the standard convention is that "bicategory" means weak and "$2$-category" means strict, but this convention doesn't generalize past "tricategory" and so forth to an arbitrary category number, and it seems perverse to have "$n$-category" mean strict by default.
2d
revised What's so special about $1$-categories?
deleted 15 characters in body
2d
answered What's so special about $1$-categories?
Dec
20
comment Purely noncommutative algebra-Morita equivalence
@truebaran: yes, that's what I meant by "the center is Morita invariant."
Dec
19
comment What is the universal property of quotienting a normaliser of the subgroup?
I should mention that when I say "in more general contexts" I have in mind the following general question: you have a functor $F : C \to D$ and an object $c \in C$ to which you apply the functor to get an object $F(c)$. What extra structure does $F(c)$ have that reflects that it was obtained in this way? Said another way, what kind of "descent data" can we attach to $F(c)$? The starting observation is that at the very least we can attach an action of the natural automorphism group or endomorphism monoid of $F$ itself, but we can go farther than this in various ways.
Dec
19
revised What is the universal property of quotienting a normaliser of the subgroup?
deleted 5 characters in body
Dec
19
awarded  Popular Question
Dec
19
comment Reconstruction Conjecture holds for Directed Acyclic Graphs?
Is there an additional meaning to the use of the word "deck" here that isn't carried by "set" (or maybe "multiset")?
Dec
19
revised What is the universal property of quotienting a normaliser of the subgroup?
added 117 characters in body
Dec
19
answered What is the universal property of quotienting a normaliser of the subgroup?
Dec
18
comment Lefschetz fixed notation
I don't see the problem. One of them has a subscript and the other doesn't.
Dec
15
awarded  Good Question
Dec
15
comment Purely noncommutative algebra-Morita equivalence
I should mention that nothing preceding the example is needed to justify the example, only to suggest where to look for it: it's clear that $\mathbb{H}$, and more generally any noncommutative division ring, is not Morita equivalent to a commutative algebra because the endomorphism algebra of every $\mathbb{H}$-module is noncommutative.
Dec
15
awarded  Nice Answer
Dec
15
comment A Category-ish Structure with Morphism Domains containing Multiple Objects?
en.wikipedia.org/wiki/Multicategory
Dec
14
answered Purely noncommutative algebra-Morita equivalence