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bio website personal.denison.edu/~whiteda
location Granville, OH
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visits member for 4 years, 8 months
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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.


4h
awarded  Archaeologist
5h
revised Stable equivalence and triangulated equivalence of self-injective algebras
fixed typos
12h
comment Kan extensions of pseudofunctors
Have you looked at Emily Riehl's book yet? My gut instinct is that she would take this approach.
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awarded  Nice Answer
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comment Injective model structure on sheaves of bounded complexes of $A$-modules
I don't have time to write a full answer just now, but I think the answer is probably yes, and that proof should use cotorsion pairs. I recommend you look at the work of Hovey and Gillespie. Gillespie has a paper handling categories of chain complexes of quasi-coherent sheaves over a scheme, and perhaps some mention is made there of the case you care about. I believe there are two cotorsion pairs in these settings, one for the projective model structure and one for the injective.
Aug
27
comment Can triangulated categories be “approximated by countable subcategories” (that are triangulated but not full!)?
Yes, it's of interest. Thanks for editing
Aug
26
reviewed Approve Precise interpretability strength of $\mathcal P_{DF}(\omega)$ and $L_{\omega_1^{CK}}$
Aug
24
comment How to compute (co)limits of enriched categories?
Giovanni Caviglia has a paper on arxiv where he computes a bunch of colimits in Cat$_V$ as part of putting a model structure on it. See also Berger-Moerdijk "On the homotopy theory of enriched categories" which Giovanni was generalizing. You ask in your last paragraph for examples and this contains some. The goal was to compute a pushout in $Cat_V$ as a transfinite composition of pushouts of things in $V$ (well, technically several copies of $V$). I think this would be a good example to work through.
Aug
24
comment How to compute (co)limits of enriched categories?
There is a paper by Kelly and Lack called "Cat$_V$ is locally presentable or locally bounded if $V$ is so" This gives you a condition under which the answer to (2) is yes. Note that asking $V$ to be locally presentable is more than asking it to be cocomplete, but often satisfied in practice. See the book of Adamek and Rosicky for more information.
Aug
20
comment Quotients of powers of the Sierpinski space
As an abstract homotopy theorist, I really like this question and I caution against closure. The Sierpinski space is a cool (counter)example and the comment of Andrej is saying something interesting about the category of topological spaces. I see no reason at all this question should be closed.
Aug
20
revised Quotients of powers of the Sierpinski space
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Aug
20
revised realization map for K-theory of spheres
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Aug
20
comment Quotients of simplicial complexes which are simplicial complexes
Doesn't the category of simplicial complexes have all small limits and colimits? Does this help? A reference is math.stackexchange.com/questions/492072/…
Aug
19
comment Composition law in the colored operad whose algebras are (symmetric) operads
You might consider looking at one of the books Donald Yau has written, e.g. his one with Mark Johnson (though Yau now has a solo-authored book on 1-colored operads too). They are very careful about spelling out how to get from the trees to the algebraic structure, including the composition law. This is a tricky step and it does not hurt to read about it in several places as you work it out.
Aug
18
comment Model structures on diagrams indexed by a Reedy category
Sure. It's basically there in Lemma 2.3.2 of Hovey's book, but obviously there are more canonical references. The oldest I can find is Grothendieck's Tohoku paper, which proves it for $R$-modules. You can get from there to chain complexes easily via the machinery in Adamek and Rosicky's book, since colimits of chain complexes are computed levelwise. See also the wikipedia article on Grothendieck categories.
Aug
18
comment Unital $A_{\infty}$-algebra?
@AmraniIlias: Wow, that is an unfortunate state of affairs. So really the OP is asking about $A_\infty$ as a reduced operad. That's fine too, and the remark about rectification still holds, but it's just annoying that the terminology doesn't line up.
Aug
18
answered Model structures on diagrams indexed by a Reedy category
Aug
18
revised Model structures on diagrams indexed by a Reedy category
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Aug
18
comment Model structures on diagrams indexed by a Reedy category
Please tell me 'totally legit' is a technical term that defines some poset property :-)
Aug
18
revised (infinity,1)-categories directly from model categories
edited body