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arXiv · 2607.01259

From orthoposets to orthomodular posets

John Harding·Gejza Jenda·Bert Lindenhovius
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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.

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John Harding, Gejza Jenda, Bert Lindenhovius. 2026-06-09. From orthoposets to orthomodular posets. https://arxiv.org/abs/2607.01259

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