Geodesic
Free objects over posemigroups in the category PoSgr_v
Theory and applications of categories, Tome 32 (2017), pp. 1098-1106.

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As we all know, the complete lattice I_D(S) of all D-ideals of a meet-semilattice S is precisely the injective hull of S in the category of meet-semilattices. In this paper, we consider sm-ideals of posemigroups which can be regarded as a generalization of D-ideals of meet-semilattices. Unfortunately, the quantale R(S) of all sm-ideals of a posemigroup S is in general not an injective hull of S. However, R(S) can be seen as a new type of quantale completions of S. Further, we can see that R(S) is also a free object over S in the category PoSgr_v of posemigroups with sm-distributive join homomorphisms.
Publié le :
Classification : 06F05, 06F07, 08B30
Keywords: partially ordered semigroup, injective hull, quantale, quantale completion, free object 
@article{TAC_2017_32_a31,
     author = {Shengwei Han and Changchun Xia and Xiaojuan Gu},
     title = {Free objects over posemigroups in the category {PoSgr_v}},
     journal = {Theory and applications of categories},
     pages = {1098--1106},
     publisher = {mathdoc},
     volume = {32},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2017_32_a31/}
}
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Shengwei Han; Changchun Xia; Xiaojuan Gu. Free objects over posemigroups in the category PoSgr_v. Theory and applications of categories, Tome 32 (2017), pp. 1098-1106. http://geodesic.mathdoc.fr/item/TAC_2017_32_a31/