PreprintCC BY 4.0arXiv
Observations on the variety of equationally linear Heyting semilattices
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 HSLat of Heyting semilattices. In this paper, we focus on the subvariety ELHSLat of equationally linear Heyting semilattices. Our main objective is to show that, unlike HSLat, this category is algebraically coherent. We furthermore prove that it is neither locally algebraically cartesian closed nor cosmash associative.
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BibTeX
@misc{garciamartinez2026observations,
title = {{Observations on the variety of equationally linear Heyting semilattices}},
author = {Xabier García-Martínez and James R. A. Gray and Michael A. Hoefnagel and Tim Van der Linden and Corentin Vienne},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.24325},
eprint = {2609.24325},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.24325},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Observations on the variety of equationally linear Heyting semilattices
AU - Xabier García-Martínez
AU - James R. A. Gray
AU - Michael A. Hoefnagel
AU - Tim Van der Linden
AU - Corentin Vienne
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.24325
UR - https://arxiv.org/abs/2609.24325
AB - 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 HSLat of Heyting semilattices. In this paper, we focus on the subvariety ELHSLat of equationally linear Heyting semilattices. Our main objective is to show that, unlike HSLat, this category is algebraically coherent. We furthermore prove that it is neither locally algebraically cartesian closed nor cosmash associative.
ER -