Quantales 作为形式概念格
Quantales as formal concept lattices
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中文总结 AI 辅助
该研究建立 Quantales、半群与形式概念分析的关联，引入定义域为半群的剩余关系，证明每个 Quantale 可作为其诱导的形式概念格，并在对应范畴间建立等价关系。
中文摘要 AI 辅助
我们建立了一座连接 Quantales、半群与形式概念分析理论的新桥梁。通过引入定义域为半群的剩余关系，我们证明每个 Quantale 都可作为此类关系诱导出的形式概念格。此外，该构造在 Quantales 范畴与以乘法结合为态射的剩余关系范畴之间建立了等价关系。
英文摘要
We establish a new bridge connecting quantales, semigroups and the theory of formal concept analysis. By introducing residuated relations whose domains are semigroups, we show that every quantale arises as the formal concept lattice induced by such a relation. Furthermore, this construction yields an equivalence between the category of quantales and a category of such residuated relations whose morphisms are multiplicative bonds.
