Liang, X., Luo, Y. (2015). Subpullbacks and coproducts of $S$-posets. Categories and General Algebraic Structures with Applications, 3(1), 1-20.

Xingliang Liang; Yanfeng Luo. "Subpullbacks and coproducts of $S$-posets". Categories and General Algebraic Structures with Applications, 3, 1, 2015, 1-20.

Liang, X., Luo, Y. (2015). 'Subpullbacks and coproducts of $S$-posets', Categories and General Algebraic Structures with Applications, 3(1), pp. 1-20.

Liang, X., Luo, Y. Subpullbacks and coproducts of $S$-posets. Categories and General Algebraic Structures with Applications, 2015; 3(1): 1-20.

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

Abstract

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.