bio  website  math.berkeley.edu/~amathew 

location  Bonn  
age  
visits  member for  5 years, 7 months 
seen  46 mins ago  
stats  profile views  20,038 
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 DGcategories 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 DGcategories 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 colimitdense 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 