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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Published in:Algebra and Discrete Mathematics
Date:2017
Main Authors: Farsad, F., Madanshekaf, A.
Format: Article
Language:English
Published: Інститут прикладної математики і механіки НАН України 2017
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/156632
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this: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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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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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.
first_indexed 2025-11-25T23:28:47Z
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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