Characterization of Epimorphisms in Archimedean Lattice-Ordered Groups and Vector Lattices

Abstract

This chapter is the first paper in a sequence of undetermined length, and this introduction is also a brief introduction to the sequence. An initial segment of that sequence is this chapter, followed by the essentially completed items listed in the bibliography as [Ball and Hager, a,b,c,d]. These papers treat various aspects of the theory of epimorphisms in the category Arch of archimedean l-groups with l-homomorphisms, and the category Wu of archimedean l-groups with distinguished weak unit and unit-preserving l-homomorphisms (and in the corresponding categories of vector lattices, which for all papers in the sequence can be disposed of with the comment: all this is true in vector lattices and the proofs require no change). Wu is itself interesting as a natural generalization of rings of continuous functions and as a setting for some functional analysis, and in any event seems to be a necessary bridge to Arch.