21,882 reputation
450170
bio website math.berkeley.edu/~theojf
location Berkeley
age 30
visits member for 5 years, 11 months
seen 13 hours ago

I am a recent graduate from UC Berkeley. Starting Fall 2013, I am a Boas Assistant Professor at Northwestern University. My research is broadly centered on quantum field theory — my interests include category theory, representation theory, homological algebra, algebraic topology, Poisson geometry, and theoretical physics.


Aug
26
comment The “$\infty$”-column in the periodic table of n-categories
Note that your gloss of the periodic table is not quite correct. For example, the full sub-2-category of Cat on the categories with 1 object is not the same as the category Alg of algebras and homomorphisms — they don't even have the same moduli spaces of objects – but rather is the same as the 2-category of algebras, homomorphisms, and natural transformations. To make the comparison precise you need to reinterpret the phrase "with one object" as including the data of how it has only one object, and functors should respect this data. This is why Rune's answer includes the word "pointed".
Aug
24
accepted Strategies for proving a category is Noetherian?
Aug
24
comment How to compute (co)limits of enriched categories?
Have you looked yet in Kelly's book? I ask because I thought he discussed (co)limits in Cat_V, but now I don't see it there...
Aug
19
comment Springer GTM Reprints in China?
There have been high profile court cases about importing Chinese printings into USA (for resale). Unfortunately, I do not recall the results. Until DMCA, though, the basic rule was that if you legally came to own a book, then that book was yours, and you could do whatever you wanted with it physically, although you could not, by default, produce copies.
Aug
16
answered How to define the internal hom between presheaves valued in cotensored categories?
Aug
10
comment Symmetric tensor powers as tensors over symmetric group algebra
I believe your presentation of the symmetric tensor power is not correct when $n\geq 3$. When $n=3$ and $\dim V = 2$ with basis $x,y$, $V^{\odot 3}$ has basis $x^3, x^2y,xy^2,y^3$ and so is 4-dimensional. The RHS is an 8-dimensional vector space quotiented by the 0-dimensional vector space, as there are no totally-antisymmetric tensors in two variables.
Aug
3
awarded  lie-algebras
Jul
31
comment Why do the model structures on dg-algebras and on dg-categories are not compatible?
At least they have the same weak equivalences. So in addition to your question --- does dgAlg have a model structure with the standard weak equivalences but the Dwyer--Kan fibrations --- one can ask whether dgCat has a model structure with its standard weak equivalences but the projective fibrations. Note that if the answers are "yes", then the identity functor will be a Quillen equivalence, which is often good enough.
Jul
30
accepted Does the following characterize local presentability?
Jul
29
asked Does the following characterize local presentability?
Jul
29
comment Frobenius $A_{\infty}$-bialgebras?
@ManuelRivera I haven't thought enough about cyclic algebras enough to confidently make any claims. Well, let me say that I would not immediately expect $u_k$ to be itself a map of bimodules (of some cohomological degree), but instead the first Taylor coefficient of a homotopy between maps of bimodules, which I think is different. Then somehow you're supposed to extract the remaining coefficients by considering signed combinations of compositions of $u_k$s and $m_j$s. At least, that's my expectation.
Jul
29
answered Frobenius $A_{\infty}$-bialgebras?
Jul
28
comment Reshetikhin-Turaev as a 3-2-1-theory
@SpicetheBird Or, you know, he could have used the Alexander invariant.
Jul
24
comment An example for a construction on monads/operads?
+1 for lots of details, definitions, theorems...
Jul
23
comment $Pin^{+}(4k)$ and $Pin^{-}(4k)$ are isomorphic [Reference Request]
The isomorphism Pin^+(4k) = Pin^-(4k) is documented in "Analysis, Manifolds and Physics. Part II" by Y. Choquet-Bruhat and C. De Witt-Morette (Elsevier, 2000). Is this what you're looking for? Note that it is not an isomorphism of groups over O(4k). (The isomorphism, as you point out, covers an interesting outer automorphism of O(4k).)
Jul
23
comment Determinant twist and $Pin _{\pm}$ structure on $4k$-dimensional bundles [Reference request]
Incidentally, I asked a related question at mathoverflow.net/questions/184982/which-real-pin-groups-agree.
Jul
22
accepted When is the adjoint to a monoidal functor monoidal?
Jul
21
comment When is the adjoint to a monoidal functor monoidal?
Of course, the answer will probably be different for different ordered pairs in {lax,oplax,strong}. For example, if $F$ is lax, it is not too hard to believe that $F^L$ is oplax, based on the way that adjoints work (e.g. we do have a canonical map $F^L(1_D) \to 1_C$ corresponding to $1_D \to F(1_C)$).
Jul
21
asked When is the adjoint to a monoidal functor monoidal?
Jul
14
awarded  Nice Answer