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http://dx.doi.org/10.5666/KMJ.2022.62.4.657

On Generators in the Category of Actions of Pomonoids on Posets and its Slices  

Farideh, Farsad (Department of Mathematics, Faculty of Mathematics, Statistics and Computer Science, Semnan University)
Ali, Madanshekaf (Department of Mathematics, Faculty of Mathematics, Statistics and Computer Science, Semnan University)
Publication Information
Kyungpook Mathematical Journal / v.62, no.4, 2022 , pp. 657-671 More about this Journal
Abstract
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;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
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