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visits member for 5 years, 9 months
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Jul
23
comment Milnor descent for ring spectra
If you are looking for the case (which I think is relevant for "Milnor descent") of a derived version of a pushout along closed immersions, there is a positive result with connectivity hypotheses in Theorem 7.2 of DAG IX, as well as a counterexample if these are omitted (Warning 7.3). As I think is implicit in your post, the functor $F$ is automatically fully faithful, so the question is equivalent to essential surjectivity of $F$ (or conservativity of $R$).
Jul
7
comment Intersections of ideals and nilpotence
@user26857: The former. I've edited to clarify this point.
Jul
7
revised Intersections of ideals and nilpotence
added 19 characters in body
Jul
7
asked Intersections of ideals and nilpotence
Jun
24
awarded  Favorite Question
May
28
awarded  Nice Question
May
24
awarded  Revival
May
24
awarded  Nice Question
May
23
answered Compact objects in undercategories and filtered colimits
Apr
26
awarded  Nice Answer
Apr
8
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Mar
16
asked Decomposition of symmetric powers of reduced regular representation modulo $p$
Mar
15
awarded  Good Answer
Mar
6
comment Explict form of $E_\infty$-morphisms between differential graded commutative algebras
So, homotopy classes of $A_\infty$-maps $A \to B$ require in addition choosing a nullhomotopy (which is a torsor over $\pi_1 B$ in this case).
Mar
6
comment Explict form of $E_\infty$-morphisms between differential graded commutative algebras
It is not true that the inclusion of $E_\infty$-algebras into $A_\infty$-algebras is fully faithful in characteristic zero. As an example, let $A$ be the (discrete) $E_\infty$-algebra $\mathbb{Q}[x,y]$ and let $B$ be an $E_\infty$-algebra with nontrivial $\pi_1$. As an $E_\infty$-algebra, $A$ is free on two generators, so homotopy classes of maps $A \to B$ give $\pi_0 B \oplus \pi_0 B$. As an $A_\infty$-algebra, $A$ is free on two generators $x,y$ together with a homotopy $xy \simeq yx$...
Feb
19
awarded  Revival
Feb
18
awarded  Nice Question
Feb
12
awarded  Nice Question
Feb
11
comment Lifting DG-categories to characteristic zero
@TylerLawson: I should clarify that I am interested in the stable case (so in your example, that would correspond to lifting modulo Morita equivalence). I am also interested in the question you raise, but I suspect there are counterexamples in the discrete case.
Feb
11
asked Lifting DG-categories to characteristic zero