On injective constructions of S-semigroups
| Authors | |
|---|---|
| Year of publication | 2019 |
| Type | Article in Periodical |
| Magazine / Source | Fuzzy Sets and Systems |
| MU Faculty or unit | |
| Citation | |
| Web | https://www.sciencedirect.com/science/article/pii/S0165011419301435?via%3Dihub |
| Doi | http://dx.doi.org/10.1016/j.fss.2019.02.012 |
| Keywords | Residuated poset; S-semigroup; Order-embedding; Subhomomorphism; Lattice-valued sup-lattice; Sup-algebra; Quantale; Q-module; S-semigroup quantale; Injective object; Injective hull; Semicategory; Quantaloid |
| Description | In this paper, we continue the study of injectivity for fuzzy-like structures. We extend the results of Zhang and Laan for partially ordered semigroups to the setting of S-semigroups. We first characterize injectives in the category Ssgr (<=) of S-semigroups with subhomomorphisms as S-semigroup quantales. Second, we show that every S-semigroup has an epsilon(<=)-injective hull, and give its concrete form. Third, connections to ordered semicategories and quantaloids are indicated. In particular, if S is a commutative quantale, then the injectives in the category of S-semigroups with subhomomorphisms generalize the quantale algebras introduced by Solovyov. Quantale algebras provide a convenient universally algebraic framework for developing lattice-valued analogues of fuzzification. (C) 2019 Elsevier B.V. All rights reserved. |
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