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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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