representation of h-closed monoreflectionsin 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 ).