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arXiv · 2609.24325

Observations on the variety of equationally linear Heyting semilattices

Xabier García-Martínez·James R. A. Gray·Michael A. Hoefnagel·Tim Van der Linden·Corentin Vienne
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Abstract

In previous work, we analysed a number of categorical properties, of interest in the context of Janelidze-Márki-Tholen semi-abelian categories, for the variety $\mathsf{HSLat}$ of Heyting semilattices. In this paper, we focus on the subvariety $\mathsf{ELHSLat}$ of equationally linear Heyting semilattices. Our main objective is to show that, unlike $\mathsf{HSLat}$, this category is algebraically coherent. We furthermore prove that it is neither locally algebraically cartesian closed nor cosmash associative.

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Xabier García-Martínez, James R. A. Gray, Michael A. Hoefnagel, Tim Van der Linden, Corentin Vienne. 2026-09-21. Observations on the variety of equationally linear Heyting semilattices. https://arxiv.org/abs/2609.24325

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