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Singular Archimedean lattice-ordered groups. (English) Zbl 0936.06015

The paper deals with the category \(W\) of all archimedean lattice-ordered groups (\(l\)-groups) with a designated weak unit and its full subcategory \(W_s\) of those \(l\)-groups in which the designated weak unit is singular. The authors also develop a necessary background in category theory concerning extension functors and contracting completion operators. Using this technique, they, for example, prove that the projectable hull in \(W_s\) is a monoreflection, characterize essential hulls in \(W_s\), describe the maximum monoreflection on \(W_s\) by contracting the corresponding monoreflection on \(W\), and analogously characterize the maximal reflection on \(W_s\).

MSC:

06F15 Ordered groups
18A40 Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.)
18A20 Epimorphisms, monomorphisms, special classes of morphisms, null morphisms
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