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 |
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
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