Starting from enriched order-theoretic properties of modules over a unital quantale in the category \(\mathsf {Sup}\), this paper presents the following theorem. If the underlying quantale is unital and involutive with a designated element, then the duality of right (left) modules preserves projectivity if and only if the underlying quantale has a dualizing element.

中文翻译：

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自对偶性下$$ \ mathsf {Sup} $$ Sup中射影模块的不变性

从类别\（\ mathsf {Sup} \）上单位量子上模块的丰富的阶理论性质开始，本文提出了以下定理。如果基础量化单元是统一的且具有指定元素，则对合（但不正确），则右（左）模块的对偶性仅当基础量化单元具有对偶元素时才保留投射性。