The Jordan-Holder theorem says that any chain of subobjects of a finite lenght object can be refined to a composition series, and that any composition series has the same lenght.
This theorem holds for any abelian category, and a notable example is the case of modules over some ring. While I do not need an example of the usefulness of J-H theorem in the context of modules, I would like to ask:
What are applications of the J-H theorem in a general abelian category, which is not (or not easily proven to be) a category of modules?