Kyungpook Mathematical Journal 2022; 62(4): 657-671
Published online December 31, 2022
Copyright © Kyungpook Mathematical Journal.
On Generators in the Category of Actions of Pomonoids on Posets and its Slices
Farideh Farsad and Ali Madanshekaf∗
Department of Mathematics, Faculty of Mathematics, Statistics and Computer Science, Semnan University, P. O. Box 35131-19111, Semnan, Iran
e-mail : faridehfarsad@yahoo.com and amadanshekaf@semnan.ac.ir
Received: November 29, 2021; Revised: May 22, 2022; Accepted: October 10, 2022
Where S is a pomonoid, let Pos-S be the category of S-posets and S-poset maps. We start off by characterizing the pomonoids S for which all projectives in this category are either generators or free. We then study the notions of regular injectivity and weakly regularly d-injectivity in this category. This leads to homological classification results for pomonoids. Among other things, we get find relationships between regular injectivity in the slice category Pos-S/BS, for any S-poset BS, and generators and cyclic projectives in Pos-S.
Keywords: S-poset, generator, projective, slice category, regular injective.
