Bounded Equivalence of Hull Classes in Archimedean Lattice-Ordered Groups with Unit

Abstract

A hull class in a category is an object class H for which each object has a unique minimal essential extension in H. This paper addresses the enormity of the collection of hull classes in the category W of Archimedean l-groups with distinguished weak order unit through consideration of the action on the hull classes of the bounded coreflection \(\textbf {W} \overset {B}\rightarrow \textbf {W}^{\ast }\) onto the subcategory where the units are strong. It is shown that hull classes go forth under B and back under B−1, that the B-equivalence class of a hull class in W always has a top, and that these B-equivalence classes are frequently not sets. The property “top” is related to various other properties that hull classes might have. This paper is the third by us on the complex taxonomy of hull classes in W, and more are planned.