TITLE: Simple object in derived category or stable model category?
QUESTION [8 upvotes]: Exist any common definition of simple objects in derived categories, or even better, in stable model categories?
I was only able to find definition for abelian categories.
Thanks.

REPLY [10 votes]: Sometimes an object $E$ of a $k$-linear category $C$ is called simple if $Hom_C(E,E) = k$. This notion is frequently used in derived categories.