bio  website  preschema.com 

location  Essen, Germany  
age  23  
visits  member for  5 years, 1 month 
seen  3 hours ago  
stats  profile views  1,246 
1d

comment 
When is the cofibrant replacement of a product the product of the cofibrant replacements?
This is true for coconnective dgalgebras, according to arxiv.org/abs/1112.2360. 
1d

answered  An example of two cofibrant dg categories whose tensor product is not cofibrant 
Jan 23 
comment 
Connection between quasifibrations and homotopy cartesian squares
Are you looking for something like this fibrewise 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 Ktheory. See for example the Goodwillie theorem, [T. Goodwillie, Relative algebraic Ktheory 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 EilenbergMac 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), 103153]. 
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
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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
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Jan 12 
revised 
Relationship between Hochschild cohomology and Drinfeld centers
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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 quasicoherent complexes from the bounded derived category of coherent sheaves, at the triangulated level. At the level of infinity or dgcategories, one can recover it as the indobjects (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 Ktheory, 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? 