Unitally nondistributive quantales
General Topology
2024-12-02 v3
Abstract
Unitally nondistributive quantales are unital quantales such that the unit is approximable by the totally below relation and does not meet-distribute over arbitrary joins. It is shown that the underlying nondistributive complete lattice contains at least elements. Moreover, under mild conditions, every quantale has an extension to a unitally nondistributive quantale by the addition of an isolated unit. As a byproduct of this construction we prove that there exist non-isomorphic, unitally nondistributive quantales on the set of elements.
Cite
@article{arxiv.2402.17284,
title = {Unitally nondistributive quantales},
author = {Javier Gutiérrez García and Ulrich Höhle},
journal= {arXiv preprint arXiv:2402.17284},
year = {2024}
}
Comments
16 pages, 8 figures