bio  website  preschema.com 

location  Essen, Germany  
age  23  
visits  member for  5 years, 3 months 
seen  5 hours ago  
stats  profile views  1,362 
7h

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. 
13h

answered  Monoidal structure on simplicial sheaves 
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 25 
awarded  Explainer 
Mar 25 
answered  Do algebraic stacks satisfy fpqc descent? 
Mar 25 
revised 
Do algebraic stacks satisfy fpqc descent?
fix link, which wasn't working 
Mar 25 
suggested  approved edit on Do algebraic stacks satisfy 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 4 
revised 
Why are pushouts the right tool in these setups
added 8 characters in body 
Mar 4 
answered  Why are pushouts the right tool in these setups 
Mar 3 
revised 
A general theory of quasifunctors, generalizing from dgcategories to $\mathcal V$categories, with $\mathcal V$ monoidal model category
added 50 characters in body 
Mar 3 
answered  A general theory of quasifunctors, generalizing from dgcategories to $\mathcal V$categories, with $\mathcal V$ monoidal model category 
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/…). 