Representation of H-closed monoreflections in archimedean l-groups with weak unit

Abstract. The category of the title is called W. This has all free objects F (I) (I a set). For an object class A, HA consists of all homomorphic images of A-objects. This note continues the study of the H-closed monoreflections (R, r) (meaning HR = R), about which we show (inter alia): A ∈ A if and only if A is a countably up-directed union from H{rF (ω)}. The meaning of this is then analyzed for two important cases: the maximum essential monoreflection r = c^3, where c^3F (ω) = C(R^ω ), and C ∈ H{c(R^ω )} means C = C(T ), for T a closed subspace of R^ω ; the epicomplete, and maximum, monoreflection, r = β, where βF (ω) = B(R^ω ), the Baire functions, and E ∈ H{B(R^ω )} means E is an epicompletion (not “the”) of such a C(T ).