Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Weak Factorization System for Actions of Po-monoids on Posets   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 $(\mathcal{C_D}, \mathcal{E_S})$ is a weak factorization system in {\bf
Pos}-$S,$ where $\mathcal{C_D}$ and $\mathcal{E_S}$ 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}-$S$.

15
The categories of this paper are: nucl-ex
20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ