The category of orthomodular posets is a full coreflective subcategory of strong orthoposets, obtained by modifying the order while preserving the underlying set and orthocomplementation; the coreflector restricts to ortholattices as a right adjoint.
Kalmbach,Orthomodular Lattices, London Mathematical Society Monographs, Vol
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From orthoposets to orthomodular posets
The category of orthomodular posets is a full coreflective subcategory of strong orthoposets, obtained by modifying the order while preserving the underlying set and orthocomplementation; the coreflector restricts to ortholattices as a right adjoint.