Weak Factorization System for Actions of Po-monoids on Posets

2014/10/17 by Farideh Farsad, Farsad, Farideh, Ali Madanshekaf +1
Mathematics · #06F05 #18A32 #18G05 #20M30 #20M50 #Category Theory (math.CT) #FOS: Mathematics #math.CT #msc:06F05 #msc:18A32 #msc:18G05 #msc:20M30 #msc:20M50

paper · pdf · doi:10.48550/arxiv.1410.5839

arxiv created 2015/04/07 · arxiv updated 2015/04/08

Abstract

Let S be a pomonoid. In this paper, \bf 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 \bf Pos-S. We show that if the identity element of S is the bottom element, then (C_D, E_S) is a weak factorization system in \bf Pos-S, where C_D and E_S are the class of down-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 \bf Pos-S/B under a particular case where B has trivial action. We get a necessary condition for regular injective objects in \bf Pos-S/B. Finally, we characterize them under a spacial case, where S is, a pogroup and conclude (Emb, Top) is a weak factorization system in \bf Pos-S.

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