Reflectors to quantales

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Authors

ZHANG Xia PASEKA Jan FENG Jianjun CHEN Yudong

Year of publication 2023
Type Article in Periodical
Magazine / Source Fuzzy Sets and Systems
MU Faculty or unit

Faculty of Science

Citation
Web
Doi http://dx.doi.org/10.1016/j.fss.2022.08.023
Keywords quantale; marked quantale; reflection; admissible subset; injective hull
Description In this paper, we show that marked quantales have a reflection into quantales. To obtain the reflection we construct free quantales over marked quantales using appropriate lower sets. A marked quantale is a posemigroup in which certain admissible subsets are required to have joins, and multiplication distributes over these. Sometimes are the admissible subsets in question specified by means of a so-called selection function. A distinguishing feature of the study of marked quantales is that a small collection of axioms of an elementary nature allows one to do much that is traditional at the level of quantales. The axioms are sufficiently general to include as examples of marked quantales the classes of posemigroups, ?-quantales, prequantales and quantales. Furthermore, we discuss another reflection to quantales obtained by the injective hull of a posemigroup.
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