bio | website | preschema.com |
---|---|---|
location | Essen, Germany | |
age | 23 | |
visits | member for | 5 years, 4 months |
seen | 6 mins ago | |
stats | profile views | 1,431 |
Feb 15 |
comment |
Descent properties of spaces
I imagine it is possible to translate everything there to model categorical language, though I can't say for sure as I haven't read the notes. Doing so would require being careful about taking (co)fibrant replacements and so on. If you are not familiar with (infinity,1)-categorical language, you can probably just read the paper keeping in mind that you should take (co)fibrant replacements whenever necessary. |
Feb 15 |
comment |
Descent properties of spaces
It looks like the author is implicitly using the language of (infinity,1)-categories. |
Feb 12 |
revised |
Algebraic K-theory and Homotopy Sheaves
added 2305 characters in body |
Feb 12 |
comment |
Algebraic K-theory and Homotopy Sheaves
@bananastack, in Thomason-Trobaugh this statement is Proposition 5.5.4. |
Feb 12 |
revised |
Algebraic K-theory and Homotopy Sheaves
added 2305 characters in body |
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 $A \otimes A^{op}$. |