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bio website preschema.com
location Essen, Germany
age 23
visits member for 5 years, 6 months
seen Jun 18 at 14:21

Mar
6
comment Explict form of $E_\infty$-morphisms between differential graded commutative algebras
Sorry, that was just a guess, and is probably wrong.
Mar
6
comment Explict form of $E_\infty$-morphisms between differential graded commutative algebras
According to Theorem 0.3 of arxiv.org/pdf/1412.1255v1.pdf, an $A_\infty$-functor between dg-categories is the same thing as a right quasi-representable bimodule. Since $A_\infty$-morphisms between commutative dg-algebras are the same thing as $E_\infty$-morphisms ($E_\infty$-alg $\hookrightarrow$ $A_\infty$-alg is fully faithful, right?), this seems to give an explicit description in terms of certain modules.
Mar
4
revised Why are pushouts the right tool in these setups
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Mar
4
answered Why are pushouts the right tool in these setups
Mar
3
revised A general theory of quasi-functors, generalizing from dg-categories to $\mathcal V$-categories, with $\mathcal V$ monoidal model category
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Mar
3
answered A general theory of quasi-functors, generalizing from dg-categories to $\mathcal V$-categories, with $\mathcal V$ monoidal model category
Mar
3
comment When does the canonical model structure on $\mathcal V$-$\mathbf{Cat}$ give a structure of monoidal model category?
dgCat is also not a monoidal model category (see mathoverflow.net/questions/195178/…).
Feb
25
comment hypothetical model structure on the category of model categories
@DmitriPavlov: the category of categories is, but I don't know about the category of model categories.
Feb
23
revised Descent properties of spaces
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Feb
23
comment Does the stable category of a nice exact category embed in (the underlying category of) a derivator?
Is your question answered by the paper webusers.imj-prg.fr/~bernhard.keller/publ/…?
Feb
22
revised Descent properties of spaces
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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
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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