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Graduate student at Northwestern. Feel free to email me at dwilson [at] u. northwestern. edu :)

Dec
17
awarded  Good Question
Dec
11
awarded  Nice Answer
Dec
11
revised Obstructions for $E_n$-algebras
added 74 characters in body
Dec
11
comment Obstructions for $E_n$-algebras
@SeanTilson You're absolutely right, of course, they start with a commutative comodule. The Dyer-Lashof operations then appear in computing the obstructions- in fact, all of the computations take place in the category of algebras in simplicial comodules over a certain simplicial operad. I'll amend the answer accordingly.
Dec
11
answered Obstructions for $E_n$-algebras
Dec
9
comment String Orientation and Level Structures
tmf_0(2) should admit an $MSO$ orientation (the Ochanine genus). I'm trying to write this down, actually, as an exercise in understanding the Ando-Hopkins-Rezk stuff.
Dec
9
answered Localizations of model categories and $\infty$-categories
Dec
9
comment Localizations of model categories and $\infty$-categories
@prefaisceau the OP is asking about the case where we start with a cellular model category, not a combinatorial one. In which case it's not at all clear that the underlying $\infty$-category is presentable.
Dec
8
comment motivation of filtered colimits
@TheoBuehler the content in SGA4 was lectured on in 1963-64, and it was published in the early 70s. In section 9 of the first lecture, Grothendieck introduces accessible categories (the idea for which he attributes to Deligne) and proves many basic results. So certainly accessible categories were around long before Lair, and it seems before Gabriel-Ulmer as well. Am I somehow confusing your historical claim?
Dec
7
comment unbounded derived category of a $\infty$-topos
nitpick: Sh^hyp(X, D(Ab)) is not a topos, but I think it's clear what you mean.
Dec
6
comment unbounded derived category of a $\infty$-topos
On the other hand, I think the two may agree if the $\infty$-topos is hypercomplete.
Dec
6
comment unbounded derived category of a $\infty$-topos
In either case the opening line "the claim is simply..." is false. While it is true that sheaves of chain complexes and chain complexes of sheaves are equivalent, this doesn't answer the OPs question. cf my comment above.
Dec
6
comment unbounded derived category of a $\infty$-topos
Lurie does not claim (and I think it might be false) that you get Spaltenstein's unbounded derived category this way. In fact, I think the whole point is that you do not, since base change fails for Spaltenstein's category. Maybe the two agree under some conditions. In any case, you do get a copy of bounded below derived category living inside.
Dec
3
comment Concrete Examples of Shimura Surfaces
en.wikipedia.org/wiki/Picard_modular_surface , en.wikipedia.org/wiki/Hilbert_modular_surface
Nov
27
comment Functoriality of the adjoint functor construction?
It seems like what you're asking is the following: "Suppose I have a cartesian fibration which is locally cocartesian, is it also cocartesian?" The answer to that question is "yes", but I may be misunderstanding your question.
Nov
8
comment Role of determinant of the matrix corresponding to $i$-th Homology group.
For (1): The trace of the matrix associated to a permutation of the basis of your vector space is precisely the number of fixed points of the permutation. For (2): Don't have much but, if you have a self-map of a torus T^n then the determinant of the map on H^1 is the map on H^n.
Oct
19
comment Do the algebras for a $\infty$-monad form a stable $\infty$-category?
On the other hand, maybe the OPs assumptions on $T$ will force the forgetful functor to preserve finite coproducts... since the forgetful functor preserves sifted colimits, this should give you the preservation of colimits that you're after. (If it works it will probably work under the weaker assumption that $T$ preserves coproducts.)
Oct
19
comment Do the algebras for a $\infty$-monad form a stable $\infty$-category?
Alg_T(C) is certainly not equivalent to its image in C! The maps are not the same.
Oct
11
answered Steenrod operations in algebraic geometry
Oct
10
awarded  Popular Question