From orthoposets to orthomodular posets

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.