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 AS over a monoid S S that can be described by means of when the functor A S ⊗− AS⊗− preserves pullbacks. In this paper, we extend these results to S 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 S -posets can be transferred to their coproducts and vice versa.