L-mosaics and orthomodular lattices

TL;DR

This paper introduces dualizable L-mosaics, a new class of hypercompositional structures, and establishes their categorical equivalence with ortholattices, offering insights into algebraic properties relevant to quantum logic.

Contribution

It defines dualizable L-mosaics and proves their categorical equivalence to ortholattices, providing a new algebraic perspective on orthomodularity.

Findings

Dualizable L-mosaics are categorically equivalent to ortholattices.

An algebraic property characterizing orthomodularity is formulated.

Potential applications to quantum logic are suggested.

Abstract

In this paper, we introduce a class of hypercompositional structures called dualizable L-mosaics. We prove that their category is equivalent to that formed by ortholattices and we formulate an algebraic property characterizing orthomodularity, suggesting possible applications to quantum logic.