Timeline for On two notions of 'generators' for a 'large' triangulated category
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 26, 2014 at 19:56 | vote | accept | Mikhail Bondarko | ||
| Jul 26, 2014 at 19:56 | comment | added | Mikhail Bondarko | Thank you! It seems that the implication you indicated is exactly what I need for my purposes. | |
| Jul 25, 2014 at 13:53 | comment | added | Leonid Positselski | The argument goes like this: suppose that the Brown representability holds for the minimal triangulated subcategory $T$ in $C$ satisfying (i). Given an object $x\in C$, consider the functor $Hom_C({-},x)$ on the category $T$ and denote by $t\in T$ an object representing it. Then the identity morphism $t\to t$ corresponds to a certain morphism $t\to x$. The cone $c$ of this morphism satisfies the negation of (ii), so it must be zero. | |
| Jul 25, 2014 at 13:26 | history | edited | Leonid Positselski | CC BY-SA 3.0 |
last sentence added
|
| Jul 25, 2014 at 13:25 | comment | added | Mikhail Bondarko | Thank you! Yes; I have met the equivalence of (i) and (ii) in the paper of Krause on well-generated triangulated categories. Yet I wonder whether well-generatedness is necessary here. | |
| Jul 25, 2014 at 13:10 | history | answered | Leonid Positselski | CC BY-SA 3.0 |