bio | website | preschema.com |
---|---|---|
location | Essen, Germany | |
age | 23 | |
visits | member for | 5 years, 8 months |
seen | Jun 18 at 14:21 | |
stats | profile views | 1,579 |
Feb
11 |
revised |
Lifting DG-categories to characteristic zero
added tag "dg-categories" |
Feb
11 |
suggested | approved edit on Lifting DG-categories to characteristic zero |
Feb
10 |
comment |
When are homotopy categories of model categories closed modules over the homotopy category of $(\infty, 1)$-categories?
@DavidWhite, the question of Hovey is about model structures on 2-categories, not about model structures on 2-relative categories. How is it relevant to this discussion? |
Feb
10 |
answered | When are homotopy categories of model categories closed modules over the homotopy category of $(\infty, 1)$-categories? |
Feb
7 |
comment |
motivation of filtered colimits
The term "compact object" surely deserves a place in this answer. |
Feb
4 |
comment |
Fourier-Mukai transforms on stacks
arxiv.org/abs/0805.0157, arxiv.org/abs/1312.7164 |
Feb
4 |
comment |
When are homotopy categories of model categories closed modules over the homotopy category of $(\infty, 1)$-categories?
Model categories enriched over SSet with the Quillen model structure are presentations of (infinity,1)-categories. Model categories enriched over SSet with the Joyal model structure are presentations of (infinity,2)-categories. See Remark 0.0.4 in [Jacob Lurie, (Infinity,2)-Categories and the Goodwillie Calculus I], arxiv.org/abs/0905.0462. |
Jan
29 |
comment |
When is the cofibrant replacement of a product the product of the cofibrant replacements?
This is true for coconnective dg-algebras, according to arxiv.org/abs/1112.2360. |
Jan
29 |
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 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 |