Weak factorization systems and fibrewise regular injectivity for actions of pomonoids on posets
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) eleme...
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| Дата: | 2017 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2017
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| Назва видання: | Algebra and Discrete Mathematics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/156632 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Weak factorization systems and fibrewise regular injectivity for actions of pomonoids on posets / F. Farsad, A. Madanshekaf // Algebra and Discrete Mathematics. — 2017. — Vol. 24, № 2. — С. 235-249. — Бібліогр.: 14 назв. — англ. |
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irk-123456789-1566322019-06-19T01:26:25Z Weak factorization systems and fibrewise regular injectivity for actions of pomonoids on posets Farsad, F. Madanshekaf, A. 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. 2017 Article Weak factorization systems and fibrewise regular injectivity for actions of pomonoids on posets / F. Farsad, A. Madanshekaf // Algebra and Discrete Mathematics. — 2017. — Vol. 24, № 2. — С. 235-249. — Бібліогр.: 14 назв. — англ. 1726-3255 2010 MSC:06F05, 18A32, 18G05, 20M30, 20M50. http://dspace.nbuv.gov.ua/handle/123456789/156632 en Algebra and Discrete Mathematics Інститут прикладної математики і механіки НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
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. |
| format |
Article |
| author |
Farsad, F. Madanshekaf, A. |
| spellingShingle |
Farsad, F. Madanshekaf, A. Weak factorization systems and fibrewise regular injectivity for actions of pomonoids on posets Algebra and Discrete Mathematics |
| author_facet |
Farsad, F. Madanshekaf, A. |
| author_sort |
Farsad, F. |
| title |
Weak factorization systems and fibrewise regular injectivity for actions of pomonoids on posets |
| title_short |
Weak factorization systems and fibrewise regular injectivity for actions of pomonoids on posets |
| title_full |
Weak factorization systems and fibrewise regular injectivity for actions of pomonoids on posets |
| title_fullStr |
Weak factorization systems and fibrewise regular injectivity for actions of pomonoids on posets |
| title_full_unstemmed |
Weak factorization systems and fibrewise regular injectivity for actions of pomonoids on posets |
| title_sort |
weak factorization systems and fibrewise regular injectivity for actions of pomonoids on posets |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2017 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/156632 |
| citation_txt |
Weak factorization systems and fibrewise regular injectivity for actions of pomonoids on posets / F. Farsad, A. Madanshekaf // Algebra and Discrete Mathematics. — 2017. — Vol. 24, № 2. — С. 235-249. — Бібліогр.: 14 назв. — англ. |
| series |
Algebra and Discrete Mathematics |
| work_keys_str_mv |
AT farsadf weakfactorizationsystemsandfibrewiseregularinjectivityforactionsofpomonoidsonposets AT madanshekafa weakfactorizationsystemsandfibrewiseregularinjectivityforactionsofpomonoidsonposets |
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2023-05-20T17:50:07Z |
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2023-05-20T17:50:07Z |
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1796154201992069120 |