bio  website  preschema.com 

location  Essen, Germany  
age  23  
visits  member for  5 years, 3 months 
seen  3 mins ago  
stats  profile views  1,369 
5h

comment 
NCG with all noncommutativity in a nilpotent ideal
In line with Qiaochu's comment, some aspects of E_ngeometry are studied in the thesis of John Francis and this sequel. 
1d

comment 
When is the category of small (pre)sheaves a(n elementary) topos?
According to this paper of Mike Shulman, when $\mathcal{P}C$ is finitely complete, it is an infinitary pretopos, so by Giraud's theorem it is a topos iff it admits a small generating set. 
Mar 27 
comment 
Is the derived category of perfect complexes idempotent complete?
In the language of infinitycategories, the relevant result is Proposition 5.5.7.8 in Higher Topos Theory. See also Section 2.4 of arxiv.org/pdf/1001.2282.pdf, especially the text right before Lemma 2.20, for a discussion adapted to the stable setting. 
Mar 27 
comment 
Is the derived category of perfect complexes idempotent complete?
One good reference is Proposition 2.1.1 here: arxiv.org/abs/math/0204218. 
Mar 25 
comment 
Do algebraic stacks satisfy fpqc descent?
@Niels, for me an algebraic stack is defined to be a sheaf of groupoids (satisfying some conditions), so I interpret the question as whether or not this sheaf satisfies fpqc descent. 
Mar 23 
comment 
When do we have $D_{\text{perf}}(\text{Qcoh}(X))\simeq D_{\text{perf}}(X)$?
The functor you write is not an equivalence, but is rather fully faithful with essential image spanned by the complexes with quasicoherent cohomology. That said, your claim is still true. I doubt that the assumptions can be relaxed, though. Verdier's counterexample in SGA 6 shows that this is unreasonable without something stronger than quasiseparated. While without quasicompactness, it is not even true that perfect complexes are cohomologically bounded. What kind of generality were you hoping for? 
Mar 13 
comment 
Brandt's definition of groupoids (1926)
What could you mean by "categories are seen as special $\infty$groupoids"? 
Mar 12 
comment 
Choice of fibrations is like a choice of a basis of a module
This is a wellknown analogy which I first learned from Chris SchommerPries's answer here: mathoverflow.net/a/78408/2503 
Mar 11 
comment 
Can motivic E_∞ring spectra be strictified to commutative motivic symmetric ring spectra?
Note: the proposition cited from Higher Algebra is now numbered 4.5.4.7 in the new version. 
Mar 6 
comment 
Explict form of $E_\infty$morphisms between differential graded commutative algebras
Sorry, that was just a guess, and is probably wrong. 
Mar 6 
comment 
Explict form of $E_\infty$morphisms between differential graded commutative algebras
According to Theorem 0.3 of arxiv.org/pdf/1412.1255v1.pdf, an $A_\infty$functor between dgcategories is the same thing as a right quasirepresentable bimodule. Since $A_\infty$morphisms between commutative dgalgebras are the same thing as $E_\infty$morphisms ($E_\infty$alg $\hookrightarrow$ $A_\infty$alg is fully faithful, right?), this seems to give an explicit description in terms of certain modules. 
Mar 3 
comment 
When does the canonical model structure on $\mathcal V$$\mathbf{Cat}$ give a structure of monoidal model category?
dgCat is also not a monoidal model category (see mathoverflow.net/questions/195178/…). 
Feb 25 
comment 
hypothetical model structure on the category of model categories
@DmitriPavlov: the category of categories is, but I don't know about the category of model categories. 
Feb 23 
comment 
Does the stable category of a nice exact category embed in (the underlying category of) a derivator?
Is your question answered by the paper webusers.imjprg.fr/~bernhard.keller/publ/…? 
Feb 22 
comment 
Descent properties of spaces
Sorry, I was probably making some mistake in my previous comment, because I wasn't able to reconstruct that argument later. 
Feb 19 
comment 
Descent properties of spaces
For your second problem, this seems to follow by applying Theorem 7.1(b) twice to the maps $X' \to Y$ and $X\to X'$, and using the facts that $Y$ is a homotopy colimit diagram and $i$ is a weak equivalence. Right? 
Feb 15 
comment 
Descent properties of spaces
Yes, but the point is that it is not an abuse of language in the world of (infinity,1)categories, because there is no issue of (co)fibrancy there. 
Feb 15 
comment 
Descent properties of spaces
I imagine it is possible to translate everything there to model categorical language, though I can't say for sure as I haven't read the notes. Doing so would require being careful about taking (co)fibrant replacements and so on. If you are not familiar with (infinity,1)categorical language, you can probably just read the paper keeping in mind that you should take (co)fibrant replacements whenever necessary. 
Feb 15 
comment 
Descent properties of spaces
It looks like the author is implicitly using the language of (infinity,1)categories. 
Feb 12 
comment 
Algebraic Ktheory and Homotopy Sheaves
@bananastack, in ThomasonTrobaugh this statement is Proposition 5.5.4. 