1,950 reputation
11427
bio website preschema.com
location Essen, Germany
age 23
visits member for 5 years, 3 months
seen 2 hours ago

Jan
23
comment Connection between quasifibrations and homotopy cartesian squares
Are you looking for something like this fibre-wise characterization: ncatlab.org/nlab/show/…?
Jan
21
awarded  Curious
Jan
20
asked Characterization of closed immersions at the level of perfect complexes
Jan
17
comment Motivation for cyclic (co)homology
One motivation for cyclic homology and its variants is the utility in computing algebraic K-theory. See for example the Goodwillie theorem, [T. Goodwillie, Relative algebraic K-theory and cyclic homology, Ann. Math. 124 (1986), 347–402].
Jan
16
comment Homological algebra is linearized homotopical algebra?
Homological algebra is the homotopy theory of chain complexes. The homotopy theory of chain complexes is equivalent to the homotopy theory of modules over the Eilenberg-Mac Lane spectrum $H\mathbf{Z}$. Hence homological algebra is a stable, linear version of the homotopy theory of spaces. See [Stefan Schwede, Brooke Shipley, Stable model categories are categories of modules, Topology 42 (2003), 103-153].
Jan
16
comment Relationship between Hochschild cohomology and Drinfeld centers
@SamuelM, according to Remark 1.5 in the paper, it seems that the Drinfeld centre of $D(A \otimes A^{op})$ will be the $\infty$-category of modules over the Hochschild chain complex of $A \otimes A^{op}$.
Jan
14
comment Relationship between Hochschild cohomology and Drinfeld centers
@SamuelM, I think I finally understood what you were really asking. I updated my answer again, let me know if that helps.
Jan
14
revised Relationship between Hochschild cohomology and Drinfeld centers
deleted 5 characters in body
Jan
13
comment Relationship between Hochschild cohomology and Drinfeld centers
@SamuelM, sorry, I wasn't very clear. I hope the updated answer is more helpful.
Jan
13
revised Relationship between Hochschild cohomology and Drinfeld centers
added 1689 characters in body
Jan
12
revised Relationship between Hochschild cohomology and Drinfeld centers
deleted 158 characters in body
Jan
12
answered Relationship between Hochschild cohomology and Drinfeld centers
Jan
12
comment Which properties of a variety are detected by its derived category of coherent sheaves?
@მამუკაჯიბლაძე, when taking into account the derived tensor product, one can recover the variety completely (this is a theorem of Thomason and Balmer).
Jan
12
comment Which properties of a variety are detected by its derived category of coherent sheaves?
As far as I know, it is not possible to recover the derived category of quasi-coherent complexes from the bounded derived category of coherent sheaves, at the triangulated level. At the level of infinity- or dg-categories, one can recover it as the ind-objects (in the regular case).
Jan
12
comment Which properties of a variety are detected by its derived category of coherent sheaves?
The derived category detects homological invariants like (higher) algebraic K-theory, Hochschild homology, cyclic homology, etc. As for cohomological invariants, it is a theorem of Orlov that these are detected up to Tate twists in general, and in some special cases detected completely.
Dec
18
awarded  Popular Question
Dec
11
awarded  Yearling
Nov
27
comment Site dependance of the Cech weak equivalences on simplicial sheaves
Just to be clear: you are asking if the weak equivalences in the model structure(s) described at ncatlab.org/nlab/show/… can be described independently of the site of definition, right?
Nov
17
revised Use of derivators to the theory of motives?
more appropriate tags
Nov
17
suggested approved edit on Use of derivators to the theory of motives?