2,154 reputation
11427
bio website preschema.com
location Essen, Germany
age 23
visits member for 5 years, 4 months
seen 14 hours ago

Apr
16
answered Does a fully faithful functor between triangulated categories induce embedding of their Grothendieck groups?
Apr
9
comment Algebraic K-theory of complex varieties
Analytic descent for K-theory would follow directly from analytic descent for perfect complexes. I have no idea whether the latter is true, though.
Apr
6
comment Integral transform on noncommutative spaces
@bananastack, I learned this from Marco Robalo's thesis, but it is probably in some paper of To\"en.
Apr
6
comment How does one compute a colimit of monoidal categories?
I believe non-strict monoidal categories can be described as algebras over a monad which is a cofibrant replacement of the monad presenting strict monoidal categories. So a similar statement should hold.
Apr
6
comment Integral transform on noncommutative spaces
@bananastack, saturated dg-categories also come from dg-algebras, by the way (from dg-algebras of finite type, even).
Apr
6
revised Integral transform on noncommutative spaces
minor correction
Apr
6
revised Integral transform on noncommutative spaces
deleted 17 characters in body
Apr
6
answered Integral transform on noncommutative spaces
Apr
5
comment What is the applications of the dg-enhancements of derived categories of sheaves
@ZhenLin, I notice now that this is made precise, in terms of dg-localization, in section 2.4 of To\"en's notes here.
Apr
4
comment What is the applications of the dg-enhancements of derived categories of sheaves
@ZhenLin, this wasn't meant to be a precise statement, but one can probably use the dg-localization or also a spectral analogue instead to make it precise.
Apr
4
answered What is the applications of the dg-enhancements of derived categories of sheaves
Apr
1
comment NCG with all noncommutativity in a nilpotent ideal
In line with Qiaochu's comment, some aspects of E_n-geometry are studied in the thesis of John Francis and this sequel.
Mar
30
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
30
answered Monoidal structure on simplicial sheaves
Mar
27
comment Is the derived category of perfect complexes idempotent complete?
In the language of infinity-categories, 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