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bio website preschema.com
location Essen, Germany
age 23
visits member for 5 years, 3 months
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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
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