Hager, A. W.; Martinez, J. Singular Archimedean lattice-ordered groups. (English) Zbl 0936.06015 Algebra Univers. 40, No. 2, 119-147 (1998). 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 \(W_s\). Reviewer: J.Rachůnek (Olomouc) Cited in 12 Documents MSC: 06F15 Ordered groups 18A40 Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.) 18A20 Epimorphisms, monomorphisms, special classes of morphisms, null morphisms Keywords:Archimedean \(l\)-group; weak unit; singular element; monoreflective subcategory PDFBibTeX XMLCite \textit{A. W. Hager} and \textit{J. Martinez}, Algebra Univers. 40, No. 2, 119--147 (1998; Zbl 0936.06015) Full Text: DOI