bio | website | preschema.com |
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location | Essen, Germany | |
age | 23 | |
visits | member for | 5 years, 3 months |
seen | 9 hours ago | |
stats | profile views | 1,342 |
Feb 22 |
comment |
Descent properties of spaces
Sorry, I was probably making some mistake in my previous comment, because I wasn't able to reconstruct that argument later. |
Feb 22 |
answered | Descent properties of spaces |
Feb 19 |
comment |
Descent properties of spaces
For your second problem, this seems to follow by applying Theorem 7.1(b) twice to the maps $X' \to Y$ and $X\to X'$, and using the facts that $Y$ is a homotopy colimit diagram and $i$ is a weak equivalence. Right? |
Feb 15 |
comment |
Descent properties of spaces
Yes, but the point is that it is not an abuse of language in the world of (infinity,1)-categories, because there is no issue of (co)fibrancy there. |
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 |
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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 |