The paper contains characterizations of generators and cyclic projective generators in the category of ordered right acts over an ordered monoid.
@article{bwmeta1.element.doi-10_2478_s11533-008-0028-6, author = {Valdis Laan}, title = {Generators in the category of S-posets}, journal = {Open Mathematics}, volume = {6}, year = {2008}, pages = {357-363}, zbl = {1166.06008}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-008-0028-6} }
Valdis Laan. Generators in the category of S-posets. Open Mathematics, Tome 6 (2008) pp. 357-363. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-008-0028-6/
[1] Anderson F., Fuller K., Rings and categories of modules, Springer-Verlag, New York-Heidelberg, 1974 | Zbl 0301.16001
[2] Bulman-Fleming S., Mahmoudi M., The category of S-posets, Semigroup Forum, 2005, 71, 443–461 http://dx.doi.org/10.1007/s00233-005-0540-y | Zbl 1095.20047
[3] Kilp M., Knauer U., Mikhalev A., Monoids acts and categories, Walter de Gruyter, Berlin, 2000 | Zbl 0945.20036
[4] Shi X., Liu Z., Wang F., Bulman-Fleming S., Indecomposable projective and flat S-posets, Comm. Algebra, 2005, 33, 235–251 http://dx.doi.org/10.1081/AGB-200040992 | Zbl 1080.20058