The main work of this paper is to investigate Q-valued lower-set Quantales,which can be regarded as a generalization of lower-set Quantales.Firstly,it is proved that the category of ordered semigroups is equivalent to the category of supercoherent Quantales.Then,it is proved that Q-valued lower-set Quantales are essentially the tensor product of lower-set Quantales and Quantale Q.
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