Geodesic
Weak factorization systems and fibrewise regular injectivity for actions of pomonoids on posets
Algebra and discrete mathematics, Tome 24 (2017) no. 2, pp. 235-249.

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Let $S$ be a pomonoid. In this paper, $\mathbf{Pos}$-$S$, 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 $\mathbf{Pos}$-$S$. We show that if $S$ is a pogroup, or the identity element of $S$ is the bottom (or top) element, then $(\mathcal{DU}, \mathrm{SplitEpi})$ is a weak factorization system in $\mathbf{Pos}$-$S$, where $\mathcal{DU}$ and $\mathrm{SplitEpi}$ 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 $\mathbf{Pos}$-$S/B$ under a particular case that $B$ has trivial action. We show that every regular injective object in $\mathbf{Pos}$-$S/B$ is topological functor. Finally, we characterize them under a special case, where $S$ is a pogroup.
Keywords: $S$-poset, slice category, regular injectivity, weak factorization system. 
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     title = {Weak factorization systems and fibrewise regular injectivity for actions of pomonoids on posets},
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     url = {http://geodesic.mathdoc.fr/item/ADM_2017_24_2_a4/}
}
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Farideh Farsad; Ali Madanshekaf. Weak factorization systems and fibrewise regular injectivity for actions of pomonoids on posets. Algebra and discrete mathematics, Tome 24 (2017) no. 2, pp. 235-249. http://geodesic.mathdoc.fr/item/ADM_2017_24_2_a4/

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