Order completions of Archimedean Riesz spaces and \(\ell\)-groups
Every Archimedean Riesz space (vector lattice) has a Dedekind completion that is essentially unique. Since the Dedekind completion has certain other nice properties (e.g. the projection property) and is easily shown to be universal in the category of Dedekind complete objects and appropriate morphisms, the existence of other completions can be demonstrated by general category theory.
scientific article; zbMATH DE number 3873397