CERTAIN EXTENSIONS AND FACTORIZATIONS OF ALPHA-COMPLETE HOMOMORPHISMSIN ARCHIMEDEAN LATTICE-ORDERED GROUPS

As a consequence of general principles, we add to the array of 'hulls' in the category Arch (of archimedean l-groups with l-homomorphisms) a nd in its non-full subcategory W (whose objects have distinguished wea k order unit, whose morphisms preserve the unit). The following discus sion refers to either Arch or W. Let alpha be an infinite cardinal num ber or infinity, let Hom(alpha) denote the class of alpha-complete hom omorphisms, and let R be a full epireflective subcategory with reflect ions denoted r(G):G --> rG. Then for each G, there is r(G)(alpha) is a n element of Hom(alpha) (G, R) such that for each phi is an element of Hom(alpha) (G, R), there is unique <(phi)over bar> with <(phi)over ba r> r(G)(alpha) = phi. Moreover if every r(G) is an essential embedding , then, for every alpha and every G, r(G)(alpha) = r(G), and every <(p hi)over bar> is an element of Hom(alpha). If alpha = omega(1) and R co nsists of all epicomplete objects, then every <(phi)over bar> is an el ement of Hom(omega 1). For alpha = infinity, and for any R, every <(ph i)over bar> is an element of Hom(infinity).