A Kind of R-Complete Category for R-Posets

In this paper we firstly construct the category CRPOS_R ^ep with objects the same as CRPOS_R (with as objects R-complete R-posets where R-limits preserve orders of approximating order family and as morphisms R-continuous mappings) and as morphisms e-p pairs. Secondly omega-chains, R-chains and R-completeness are defined in CRPOS_R ^ep. They are generalizations of omega-chains and omega-completeness in poset. Thirdly we give a kind of characterizations of R-limit in CRPOS_R ^ep. Finally we prove that CRPOS_R ^ep is R-complete. It is worth pointing out that a R-limit construction in CRPOS_R ^ep is given in this work.