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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| Опубліковано в: : | Algebra and Discrete Mathematics |
|---|---|
| Дата: | 2017 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2017
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| Онлайн доступ: | https://nasplib.isofts.kiev.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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862561878057680896 |
|---|---|
| author | Farsad, F. Madanshekaf, A. |
| author_facet | Farsad, F. Madanshekaf, A. |
| 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. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| 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.
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| first_indexed | 2025-11-25T23:28:47Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-156632 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-11-25T23:28:47Z |
| publishDate | 2017 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Farsad, F. Madanshekaf, A. 2019-06-18T18:07:06Z 2019-06-18T18:07:06Z 2017 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. https://nasplib.isofts.kiev.ua/handle/123456789/156632 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. The authors are very grateful to the anonymous referee for reading the paper at least twice and giving very helpful suggestions. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics Weak factorization systems and fibrewise regular injectivity for actions of pomonoids on posets Article published earlier |
| spellingShingle | Weak factorization systems and fibrewise regular injectivity for actions of pomonoids on posets Farsad, F. Madanshekaf, A. |
| title | 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_short | 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 |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/156632 |
| work_keys_str_mv | AT farsadf weakfactorizationsystemsandfibrewiseregularinjectivityforactionsofpomonoidsonposets AT madanshekafa weakfactorizationsystemsandfibrewiseregularinjectivityforactionsofpomonoidsonposets |