Orthomodular posets are algebras over bounded posets with involution
Gejza Jen\v{c}a
TL;DR
This paper establishes a formal algebraic relationship between orthomodular posets and bounded posets with involution, showing they are connected through a monadic adjunction.
Contribution
It proves that orthomodular posets can be characterized as algebras over bounded posets with involution via a monadic adjunction.
Findings
Existence of a monadic adjunction between the categories
Orthomodular posets as algebras over bounded posets with involution
Formal categorical framework for orthomodular posets
Abstract
We prove that there is a monadic adjunction between the category of bounded posets with involution and the category of orthomodular posets.
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