5,901 reputation
33666
bio website personal.denison.edu/~whiteda
location Middletown, CT
age
visits member for 4 years, 6 months
seen 23 mins ago

I am an assistant professor at Denison University. I completed my PhD at Wesleyan University in 2014 under the supervision of Mark Hovey, and I completed a masters degree in computer science under the supervision of Danny Krizanc. I'm mostly interested in questions involving (semi) model categories, Bousfield localization, and algebras over (colored) operads. I like to apply my work to stable, equivariant, and motivic homotopy theory. On the computer science side I like thinking about graph theory, probability, and social networks, with an eye towards algorithms. I've also begun to dabble in game theory and economics.


14h
revised Can triangulated categories be “approximated by countable subcategories” (that are triangulated but not full!)?
edited title
16h
comment On combinatorial and cellular model categories and infinity categories
Awesome, thanks! I knew that paper, but somehow did not know that result.
1d
comment On combinatorial and cellular model categories and infinity categories
I edited to clarify what I wanted regarding (2), i.e. cofibrantly generated but not cellular. I didn't mean it as a subquestion of (1). So I think pro-categories answer (3) nicely and your example of a pro category of a large finitely complete and cocomplete $\infty$-category seems to answer (1) very nicely.
1d
comment On combinatorial and cellular model categories and infinity categories
Any luck finding that reference from Dugger? Also, I clarified what I was looking for in (2), i.e. something cofibrantly generated but not cellular. Pro categories seem to be a really nice example
1d
revised On combinatorial and cellular model categories and infinity categories
Clarified (2)
1d
revised On combinatorial and cellular model categories and infinity categories
edited body
1d
revised Model for the (infinity,1)-category of (homotopy-)limit preserving functors
added 1 character in body
Jun
26
comment Cellular model structures on continuous functors
In your first comment you say that evaluating a cell complex only gives a sequence of h-cofibrations. I don't think that's quite right. The generating cofibrations are objectwise cofibrations in Top, and colimits are computed objectwise, so any cell complex will be an objectwise cofibration. In particular, you do know that when you evaluate a cell complex (a.k.a. a presentation of T) that every map is an objectwise cofibration, and I use that in the proof below. The proof is probably still valid with objectwise h-cofibrations, but I wanted to avoid that generality
Jun
26
revised Cellular model structures on continuous functors
Finally found a complete proof
Jun
24
revised What are the benefits of viewing a sheaf from the “espace étalé” perspective?
fixed typos since it was on the front page anyway
Jun
24
revised What are the benefits of viewing a sheaf from the “espace étalé” perspective?
fixed typos since it was on the front page anyway
Jun
23
comment On combinatorial and cellular model categories and infinity categories
I found a place where the dual came up naturally: mathoverflow.net/questions/117267/…
Jun
20
comment On combinatorial and cellular model categories and infinity categories
Hi Dylan. Thanks for your answer. Can you give a precise reference for (1)? If I ever learned that result before I must have forgotten it. Regarding (3), I like the pro example. Can you think of a specific instance when the opposite of a presentable $\infty$-category was needed? I can't seem to think of a time anyone needed the opposite of a combinatorial model category.
Jun
20
revised On combinatorial and cellular model categories and infinity categories
edited in response to a comment
Jun
20
comment On combinatorial and cellular model categories and infinity categories
Dear Tyler: yes, I think it would be good to assume that for the purpose of this question. Of course, if it's lacking one can still ask for a model structure in the sense of Hovey's book rather than a model category but I don't feel the need to get into that right now. So I'll edit to make it clear I want things to be bicomplete, and thanks for pointing this out
Jun
19
comment Localizations of model categories and $\infty$-categories
I am not so sure that you can remove the requirement about being simplicial. This doesn't feel like the sort of situation where it's just a choice of framing. Rather, Lurie's nice adjunction you mention seems to need the simplicial hypothesis in a stronger way. I guess what I'm saying is: I'd love to see someone actually do that work to remove the simplicial hypothesis, because I think I'd learn something from it.
Jun
19
comment On combinatorial and cellular model categories and infinity categories
I should advertise that a related question is: mathoverflow.net/questions/189301/…
Jun
19
asked On combinatorial and cellular model categories and infinity categories
Jun
19
revised Compact open topology on $\mathrm{Homeo}(X)$
fixed typos since it was on the front page anyway
Jun
17
revised Does the CGWH-fication change the (weak) homotopy type?
edited body