Subpullbacks and Po-flatness Properties of S-posets

In (golchin a. and rezaei p., subpullbacks and flatness properties of s-posets. comm. algebra. 37: 1995-2007 (2009)) study was initiated of flatness properties of right s-posets a_s over a pomonoid s that can be described by surjectivity of ? corresponding to certain (sub)pullback diagrams and new properties such as ?(pwp)?_w and ?(wp)?_w were discovered. in this article first of all we describe po-flatness properties of s-posets over pomonoids by po-surjectivity of ? corresponding to certain subpullback diagrams. then we introduce three new conditions (p_sw), ?(wp)?_sw and ?(pwp)?_sw and investigate the relation between them and conditions (p), (p_w), (wp), ?(wp)?_w, (pwp) and ?(pwp)?_w. also we describe these properties by po-surjectivity of ? corresponding to certain subpullback diagrams and describe conditions (p_w), ?(wp)?_w and ?(pwp)?_w by weak po-surjectivity of ? corresponding to certain subpullback diagrams.