عنوان مجله
|
Quasigroups and Related Systems
|
چکیده
|
In this paper, after recalling the category PosAct-S of all poset acts over
a pomonoid S; an S-act in the category Pos of all posets, with action preserving monotone maps between them, some categorical properties of the category PosAct-S are
considered. In particular, we describe limits and colimits such as products, coproducts,
equalizers, coequalizers and etc. in this category. Also, several kinds of epimorphisms
and monomorphisms are characterized in PosAct-S. Finally, we study injectivity and
projectivity in PosAct-S with respect to (regular) monomorphisms and (regular) epimorphisms, respectively, and see that although there is no non-trivial injective poset act
with respect to monomorphisms, PosAct-S has enough regular injectives with respect to
regular monomorphisms. Also, it is proved that regular injective poset acts are exactly
retracts of cofree poset acts over complete posets.
|