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The Jordan-Holder theorem says that any chain of subobjects of a finite length object can be refined to a composition series, and that any composition series has the same length.

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 JH theorem in the context of modules, I would like to ask:

What are applications of the JH theorem in a general abelian category, which is not (or not easily proven to be) a category of modules?

[This question was originally asked on mathstackexchange, but it received upvotes with no answers. I think it is more likely it will get interesting answers on this site.]

The Jordan-Holder theorem says that any chain of subobjects of a finite length object can be refined to a composition series, and that any composition series has the same length.

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 JH theorem in the context of modules, I would like to ask:

What are applications of the JH theorem in a general abelian category, which is not (or not easily proven to be) a category of modules?

[originally asked on mathstackexchange]

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 JH theorem in the context of modules, I would like to ask:

What are applications of the JH theorem in a general abelian category, which is not (or not easily proven to be) a category of modules?

[This question was originally asked on mathstackexchange, but it received upvotes with no answers. I think it is more likely it will get interesting answers on this site.]

The Jordan-Holder theorem says that any chain of subobjects of a finite length object can be refined to a composition series, and that any composition series has the same length.

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 JH theorem in the context of modules, I would like to ask:

What are applications of the JH theorem in a general abelian category, which is not (or not easily proven to be) a category of modules?

[This question was originally asked on mathstackexchange, but it received upvotes with no answers. I think it is more likely it will get interesting answers on this site.]