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Title: | Weak factorization systems and fibrewise regular injectivity for actions of pomonoids on posets |
Authors: | Farsad, F. Madanshekaf, A. |
Keywords: | S-poset slice category regular injectivity weak factorization system. |
Issue Date: | 2017 |
Publisher: | ДЗ "Луганський національний університет імені Тараса Шевченка" |
Series/Report no.: | Математичні науки; |
Abstract: | Let S be a pomonoid. In this paper, Pos-S, the category of S-posets and S-poset maps, is considered. One of the main aims of this paper is to draw attention to the notion of weak factorization systems in Pos-S. We show that if S is a pogroup, or the identity element of S is the bottom (or top) element, then (DU, SplitEpi) is a weak factorization system in Pos-S, where DU and SplitEpi are the class of du-closed embedding S-poset maps and the class of all split S-poset epimorphisms, respectively. Among other things, we use a fibrewise notion of complete posets in the category Pos-S/B under a particular case that B has trivial action. We show that every regular injective object in Pos-S/B is topological functor. Finally, we characterize them under a special case, where S is a pogroup. |
Description: | Farsadт F. Weak factorization systems and fibrewise regular injectivity for actions of pomonoids on posets / F. Farsad, A. Madanshekaf // Algebra and Discrete Mathematics. - 2017. - Vol. 24. - Number 2. - Рp. 235-249 |
URI: | http://hdl.handle.net/123456789/4551 |
Appears in Collections: | Algebra and Discrete Mathematics. - № 2 (24). - 2017 |
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