Orthomodularity of Decompositions in a Categorical Setting
- 51 Downloads
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 Wordsorthomodular poset orthoalgebra decomposition product category
Unable to display preview. Download preview PDF.
- Abramsky, S. and Coecke, B. (2004). A categorical semantics of quantum protocols, Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science: LICS 2004, IEEE Computer Society, pp.415–425.Google Scholar
- Kalmbach, G. (1983). Orthomodular Lattices, Academic Press.Google Scholar
- Pták, P. and Pulmannová, S. (1991). Orthomodular Structures as Quantum Logics. Fundamental Theories of Physics, 44, Kluwer, Dordrecht.Google Scholar