A Dagger Kernel Category of Complete Orthomodular Lattices
| Autoři | |
|---|---|
| Rok publikování | 2025 |
| Druh | Článek v odborném periodiku |
| Časopis / Zdroj | International Journal of Theoretical Physics |
| Fakulta / Pracoviště MU | |
| Citace | |
| www | https://link.springer.com/article/10.1007/s10773-025-05965-z |
| Doi | https://doi.org/10.1007/s10773-025-05965-z |
| Klíčová slova | Quantum logic; Complete orthomodular lattice; Categorical logic; Dagger kernel category |
| Popis | 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. |
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