From orthoposets to orthomodular posets

John Harding; Gejza Jenda; Bert Lindenhovius

From orthoposets to orthomodular posets

Combinatorics 2026-06-09 v1 Mathematical Physics Category Theory Quantum Physics

Authors: John Harding , Gejza Jenda , Bert Lindenhovius

Abstract

We show that the category of orthomodular posets is a full coreflective subcategory of the category of strong orthoposets, those orthoposets in which any two orthogonal elements have a join. This coreflection is obtained by building from a strong orthoposet $P$ , an orthomodular poset with the same underlying set and same orthocomplementation as $P$ , but with modified order. This coreflector restricts to a functor from the category of ortholattices to the category of orthomodular posets, and this functor is right adjoint.

Cite

@article{arxiv.2607.01259,
  title  = {From orthoposets to orthomodular posets},
  author = {John Harding and Gejza Jenda and Bert Lindenhovius},
  journal= {arXiv preprint arXiv:2607.01259},
  year   = {2026}
}