Timeline for Name for abelian category in which every short exact sequence splits
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Apr 13, 2019 at 11:31 | history | edited | Leonid Positselski | CC BY-SA 4.0 |
added the requirement that a simple object must be nonzero; mentioned Jeremy's comment establishing that all semisimple categories are split
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| Apr 13, 2019 at 11:24 | comment | added | Leonid Positselski | A semisimple Grothendieck abelian category is another name for a discrete spectral category. It would be interesting to know whether there exist semisimple abelian categories with coproducts and a generator that are not Grothendieck. | |
| Apr 13, 2019 at 11:21 | comment | added | Leonid Positselski | @JeremyRickard Thank you, yes, you are right. So every semisimple abelian category is split. | |
| Apr 13, 2019 at 7:59 | comment | added | Jeremy Rickard | Regarding “Is every semisimple abelian category split?”: If every object is a coproduct of simples, can you not directly construct a splitting of an epimorphism $f:X\to Y$ by decomposing $Y$ as a coproduct of simples $S$ and then for each $S$ decomposing $f^{-1}(S)$ as a coproduct of simples? | |
| Apr 13, 2019 at 1:14 | comment | added | Donu Arapura | OK, good to know. I withdraw my earlier suggestion. | |
| Apr 13, 2019 at 0:28 | history | answered | Leonid Positselski | CC BY-SA 4.0 |