International Journal of Theoretical Physics

, Volume 45, Issue 6, pp 1079–1090 | Cite as

Orthomodularity of Decompositions in a Categorical Setting

  • John Harding
Article

Abstract

We provide a method to construct a type of orthomodular structure known as an orthoalgebra from the direct product decompositions of an object in a category that has finite products and whose ternary product diagrams give rise to certain pushouts. This generalizes a method to construct an orthomodular poset from the direct product decompositions of familiar mathematical structures such as non-empty sets, groups, and topological spaces, as well as a method to construct an orthomodular poset from the complementary pairs of elements of a bounded modular lattice.

Key Words

orthomodular poset orthoalgebra decomposition product category 

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Copyright information

© Springer Science + Business Media, Inc. 2006

Authors and Affiliations

  • John Harding
    • 1
  1. 1.New Mexico State UniversityLas CrucesNew Mexico

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