Subpullbacks and coproducts of S-posets

In 2001, s. bulman-fleming et al. initiated the study of three flatness properties (weakly kernel flat, principally weakly kernel flat, translation kernel flat) of right acts a_{s} over a monoid s that can be described by means of when the functor a_{s} otimes - preserves pullbacks. in this paper, we extend these results to s-posets and present equivalent descriptions of weakly kernel po-flat, principally weakly kernel po-flat and translation kernel po-flat. moreover, we show that most of flatness properties of s-posets can be transferred to their coproducts and vice versa.