Singular Archimedean lattice-ordered groups
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 \(W_s\).
scientific article; zbMATH DE number 1407108