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@article{2252429,
author = {Zhang, Xia and Paseka, Jan and Feng, Jianjun and Chen, Yudong},
article_number = {March},
doi = {http://dx.doi.org/10.1016/j.fss.2022.08.023},
keywords = {quantale; marked quantale; reflection; admissible subset; injective hull},
language = {eng},
issn = {0165-0114},
journal = {Fuzzy Sets and Systems},
title = {Reflectors to quantales},
url = {https://doi.org/10.1016/j.fss.2022.08.023},
volume = {455},
year = {2023}
}
TY - JOUR
ID - 2252429
AU - Zhang, Xia - Paseka, Jan - Feng, Jianjun - Chen, Yudong
PY - 2023
TI - Reflectors to quantales
JF - Fuzzy Sets and Systems
VL - 455
IS - March
SP - 102-123
EP - 102-123
PB - Elsevier
SN - 01650114
KW - quantale
KW - marked quantale
KW - reflection
KW - admissible subset
KW - injective hull
UR - https://doi.org/10.1016/j.fss.2022.08.023
N2 - 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, σ-quantales, prequantales and quantales. Furthermore, we discuss another reflection to quantales obtained by the injective hull of a posemigroup.
ER -
ZHANG, Xia, Jan PASEKA, Jianjun FENG and Yudong CHEN. Reflectors to quantales. \textit{Fuzzy Sets and Systems}. Elsevier, 2023, vol.~455, March, p.~102-123. ISSN~0165-0114. Available from: https://dx.doi.org/10.1016/j.fss.2022.08.023.
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