10,491 reputation
443133
bio website math.berkeley.edu/~amathew
location Bonn
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visits member for 5 years, 7 months
seen 46 mins ago

12h
awarded  Revival
12h
awarded  Nice Question
1d
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
Jan
26
asked Can any object in a presentable category be written as a colimit of generators?
Jan
24
awarded  Necromancer