Composition series of arbitrary cardinality in modular lattices and abelian categories

For a certain family of complete modular lattices, we prove Jordan--H\"older--Scheier-like" theorem with no assumptions on cardinality or well-orderedness. This includes both lattices which are join- and meet-continuous, as well the subobjects any object in an abelian category satisfying properties related to Grothendieck's axioms (AB5) (AB5*). We then give several examples objects categories satisfy these axioms, including pointwise finite-dimensional persistence modules, presheaves, Pr\"ufer modules. Moreover, show that, over arbitrary ring, infinite product isomorphic simple modules fails our admits at least two composition series distinct cardinalities. conclude by giving lattice-theoretic proof that is locally finitely generated satisfies can be expressed direct sum indecomposable subobjects. conjecture this decomposition unique.