bio | website | preschema.com |
---|---|---|
location | Essen, Germany | |
age | 23 | |
visits | member for | 5 years, 4 months |
seen | 2 hours ago | |
stats | profile views | 1,446 |
Mar 25 |
revised |
Do algebraic stacks satisfy fpqc descent?
fix link, which wasn't working |
Mar 25 |
suggested | approved edit on Do algebraic stacks satisfy fpqc descent? |
Mar 23 |
comment |
When do we have $D_{\text{perf}}(\text{Qcoh}(X))\simeq D_{\text{perf}}(X)$?
The functor you write is not an equivalence, but is rather fully faithful with essential image spanned by the complexes with quasi-coherent cohomology. That said, your claim is still true. I doubt that the assumptions can be relaxed, though. Verdier's counterexample in SGA 6 shows that this is unreasonable without something stronger than quasi-separated. While without quasi-compactness, it is not even true that perfect complexes are cohomologically bounded. What kind of generality were you hoping for? |
Mar 13 |
comment |
Brandt's definition of groupoids (1926)
What could you mean by "categories are seen as special $\infty$-groupoids"? |
Mar 12 |
comment |
Choice of fibrations is like a choice of a basis of a module
This is a well-known analogy which I first learned from Chris Schommer-Pries's answer here: mathoverflow.net/a/78408/2503 |
Mar 11 |
comment |
Can motivic E_∞-ring spectra be strictified to commutative motivic symmetric ring spectra?
Note: the proposition cited from Higher Algebra is now numbered 4.5.4.7 in the new version. |
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
added 8 characters in body |
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
added 50 characters in body |
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
added 86 characters in body |
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
added 335 characters in body |
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? |