A new perspective on the tensor product of semi-lattices

TL;DR

This paper introduces a novel approach to tensor products of semi-lattices using bi-extensional Chu spaces, comparing it with existing methods and exploring its properties.

Contribution

It presents a new perspective on tensor products of semi-lattices via Chu spaces, extending the understanding beyond the canonical tensor product.

Findings

Comparison with Fraser's tensor product in distributive and general cases

Properties of the new tensor product are established

Provides a unified framework for semi-lattice tensor products

Abstract

We adopt a new perspective on the tensor product of arbitrary semi-lattices. Our basic construction exploits a description of semi-lattices in terms of bi-extensional Chu spaces associated to a target space defined to be the boolean domain. The comparison between our tensor product and the canonical tensor product, introduced by G.A. Fraser, is made in the distributive case and in the general case. Some properties of our tensor products are also given.