Semilattices with a congruence

Paolo Lipparini

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arXiv · 2407.08446

Semilattices with a congruence

Paolo Lipparini

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Abstract

A specialization semilattice is a semilattice together with a coarser preorder satisfying a compatibility condition. We show that the category of specialization semilattices is isomorphic to the category of semilattices with a congruence, hence equivalent to the category of semilattice epimorphisms. Guided by the above example, we recall an ``internal'' characterization of surjective homomorphisms between general relational systems.

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Paolo Lipparini. 2025-07-11. Semilattices with a congruence. https://arxiv.org/abs/2407.08446

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