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arXiv · 2609.13809

Concept lattices of $Q$-relations via diagonal and back-diagonal categories

Hongliang Lai·Bo Pang
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Abstract

Let $Q$ be a commutative unital quantale and $\QRel$ the ordered category of sets and $Q$-relations. We develop a categorical foundation for formal and property-oriented concept lattices of $Q$-relations via the diagonal category $\DQRel$ and back-diagonal category $\BQRel$. Our main results are: (1) the formal concept lattice construction is induced by a representable functor on $\BQRel$; (2) the property-oriented concept lattice construction corresponds to a representable functor on $\DQRel$; and (3) for regular $Q$-relations, the property-oriented concept lattice of their pointwise tensor product is naturally isomorphic to the tensor product of the respective property-oriented concept lattices.

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Hongliang Lai, Bo Pang. 2026-09-12. Concept lattices of $Q$-relations via diagonal and back-diagonal categories. https://arxiv.org/abs/2609.13809

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