Subpullbacks and coproducts of S-posets

In ۲۰۰۱, 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.

Keywords:

S-poset , subpullback , flatness , coproduct