Subpullbacks and coproducts of $S$-posets

Document Type: Research Paper


School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, PR China.


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.


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