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arXiv · 2608.26631

Quantales as formal concept lattices

Lili Shen·Xiaojuan Zhao
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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.

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Lili Shen, Xiaojuan Zhao. 2026-08-27. Quantales as formal concept lattices. https://arxiv.org/abs/2608.26631

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