A Dagger Kernel Category of Complete Orthomodular Lattices
| Authors | |
|---|---|
| Year of publication | 2025 |
| Type | Article in Periodical |
| Magazine / Source | International Journal of Theoretical Physics |
| MU Faculty or unit | |
| Citation | |
| web | https://link.springer.com/article/10.1007/s10773-025-05965-z |
| Doi | https://doi.org/10.1007/s10773-025-05965-z |
| Keywords | Quantum logic; Complete orthomodular lattice; Categorical logic; Dagger kernel category |
| Description | Dagger kernel categories, a powerful framework for studying quantum phenomena within category theory, provide a rich mathematical structure that naturally encodes key aspects of quantum logic. This paper focuses on the category {\textbf {SupOMLatLin}} of complete orthomodular lattices with linear maps. We demonstrate that {\textbf {SupOMLatLin}} itself forms a dagger kernel category, equipped with additional structure such as dagger biproducts and free objects. A key result establishes a concrete description of how every morphism in {\textbf {SupOMLatLin}} admits an essentially unique factorization as a zero-epi followed by a dagger monomorphism. This factorization theorem, along with the dagger kernel category structure of {\textbf {SupOMLatLin}}, provides new insights into the interplay between complete orthomodular lattices and the foundational concepts of quantum theory. |
| Related projects: |