10,556 reputation
444134
bio website math.berkeley.edu/~amathew
location Bonn
age
visits member for 5 years, 8 months
seen 5 hours ago

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
awarded  Nice Question
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
Jan
26
accepted Can any object in a presentable category be written as a colimit of generators?
Jan
26
comment Can any object in a presentable category be written as a colimit of generators?
Todd and @MikeShulman, thanks for explaining this.
Jan
26
comment Can any object in a presentable category be written as a colimit of generators?
Interesting. Could you (or Mike) perhaps elaborate why $\mathbb{2}$ is not a colimit-dense generator in $Cat$?
Jan
26
revised Can any object in a presentable category be written as a colimit of generators?
added 480 characters in body; edited title