bio | website | math.berkeley.edu/~amathew |
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location | Bonn | |
age | ||
visits | member for | 5 years, 8 months |
seen | 5 hours ago | |
stats | profile views | 20,339 |
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 |