Timeline for Simple object in derived category or stable model category?
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 26, 2015 at 17:46 | comment | added | Nuno | I may be missing something simple, but to justify your last sentence shouldn't we require that the triangulated category is Karoubian? | |
| Jul 11, 2011 at 22:45 | comment | added | David E Speyer | In my experience (coming mostly from the quiver theory literature), this definition isn't popular because there are very few monomorphisms in the derived category. For example, if $R$ is a ring, and $0 \to M_1 \to M_2 \to M_3 \to 0$ is a non-split s.e.s. of $R$-modules, then $M_1 \to M_2$ is not a monomorphism in the derived category of $R$-modules. In my reading, Sasha's definition is the standard one. | |
| Jul 11, 2011 at 19:28 | comment | added | Ralph | Good explanation. It seems to me, this definition even works in every category with a zero object, not just abelian categories. But perhaps I'm missing something ? | |
| Jul 11, 2011 at 17:55 | history | answered | Neil Strickland | CC BY-SA 3.0 |