An axiomatic characterization of the Gabriel-Roiter measure
arXiv:math/0604202
Abstract
Given an abelian length category A, the Gabriel-Roiter measure with respect to a length function l is characterized as a universal morphism ind(A)-->P of partially ordered sets. The map is defined on the isomorphism classes of indecomposable objects of A and is a suitable refinement of the length function l.
9 pages, final version, to appear in Bull. London Math. Soc