The Category of Archimedean ℓ-Groups With Strong Unit, and Some of its Epireflective Subcategories

Abstract

This paper explicates some basic categorical ideas in the category of the title, W ^∗ (e.g., products and coproducts, monics, epics, and extremal monics, …) for the record, and for immediate application to description of some epireflective subcategories generated in various ways (at least six) by subobjects E of the reals $\mathbb {R}$. These E have a very special place in W ^∗ because of the Yosida Representation G ≤ C(Y G) which says directly that $\mathbb {R}$ is a co-separator in W ^∗, and implies less directly that G ≤ C(Y G) is the epicomplete monoreflection of G. The E are exactly the nonterminal quasi-initial objects of W ^∗ and generate the atoms in the lattice of epireflective subcategories of W ^∗.