L-mosaics and orthomodular lattices

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. To achieve this, we establish an equivalence between the category of bounded join-semilattices and that of L-mosaics, thereby providing a categorical foundation for our framework.