Reflectors to quantales

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Publikace nespadá pod Filozofickou fakultu, ale pod Přírodovědeckou fakultu. Oficiální stránka publikace je na webu muni.cz.
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ZHANG Xia PASEKA Jan FENG Jianjun CHEN Yudong

Rok publikování 2023
Druh Článek v odborném periodiku
Časopis / Zdroj Fuzzy Sets and Systems
Fakulta / Pracoviště MU

Přírodovědecká fakulta

Citace
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Doi http://dx.doi.org/10.1016/j.fss.2022.08.023
Klíčová slova quantale; marked quantale; reflection; admissible subset; injective hull
Popis 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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