Year: 2026
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Shen, Lili, Zhao, Xiaojuan
Institutions: Sichuan University, Southwest Jiaotong University
Topic: Advanced Algebra and Logic
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204564662
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