Author： Harding John
Publisher： Springer Publishing Company
ISSN： 0020-7748
Source： International Journal of Theoretical Physics, Vol.45, Iss.6, 2006-06, pp. : 1079-1090
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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.
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