Essential completeness of archimedean ℓ-groups with weak order unit

It is shown that (1) the property of a category of having unique essential completions is inherited by any monocoreflective subcategory whose monics are monic in the larger category provided the essential monomorphisms of the latter satisfy a certain condition, and (2) the category W of archimedean ℓ-groups with weak order unit is of that type. Then, identification is made of various such subcategories of W and their essential completions are analysed. The methods exploit the functors from these categories to categories of frames.