Directed colimits of some flatness properties and purity of epimorphisms in S-posets

Abstract

Let S be a pomonoid. In this paper, we introduce some new types of epimorphisms with certain purity conditions, and obtain equivalent descriptions of various flatness properties of S-posets, such as strong flatness, Conditions (E), (E′), (P), (Pw), (WP), (WP)w, (PWP) and (PWP)w. Thereby, we present other equivalent conditions in the Stenström-Govorov-Lazard theorem for S-posets. Furthermore, we prove that these new epimorphisms are closed under directed colimits. Meantime, this implies that by a new approach we can show that most of flatness properties of S-posets can be transferred to their directed colimit. Finally, we prove that every class of S-posets having a flatness property is closed under directed colimits.

A study on strongly convex hyper S-subposets in hyper S-posets

“…A Right S-posets can be defined analogously. Preliminary work on S-posets was carried out by Fakhruddin in the 1980s (see [4,5]) and continued in recent papers, for example, see [6][7][8][9][10][11][12][13][14]. Also see [15] for an overview.…”