A Dagger Kernel Category of Complete Orthomodular Lattices

J 2025

A Dagger Kernel Category of Complete Orthomodular Lattices

BOTUR, Michal; Jan PASEKA a Richard SMOLKA

Základní údaje

Originální název

A Dagger Kernel Category of Complete Orthomodular Lattices

Autoři

BOTUR, Michal; Jan PASEKA a Richard SMOLKA

Vydání

International Journal of Theoretical Physics, Springer, 2025, 0020-7748

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

10101 Pure mathematics

Stát vydavatele

Spojené státy

Utajení

není předmětem státního či obchodního tajemství

Odkazy

URL

Impakt faktor

Impact factor: 1.700 v roce 2024

Označené pro přenos do RIV

Ano

Kód RIV

RIV/00216224:14310/25:00141910

Organizační jednotka

Přírodovědecká fakulta

Klíčová slova anglicky

Quantum logic; Complete orthomodular lattice; Categorical logic; Dagger kernel category

Štítky

14311010, rivok

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 1. 9. 2025 11:55, Mgr. Marie Novosadová Šípková, DiS.

Anotace

V originále

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.

Návaznosti

GF25-20013L, projekt VaV

Název: Ortogonalita a symetrie

Investor: Grantová agentura ČR, Ortogonalita a symetrie, Partnerská agentura

MUNI/A/1457/2023, interní kód MU

Název: Specifický výzkum v odborné, aplikované a učitelské matematice 2024

Investor: Masarykova univerzita, Specifický výzkum v odborné, aplikované a učitelské matematice 2024

Citovat

BOTUR, Michal; Jan PASEKA a Richard SMOLKA. A Dagger Kernel Category of Complete Orthomodular Lattices. International Journal of Theoretical Physics. Springer, 2025, roč. 64, č. 5, s. 1-16. ISSN 0020-7748. Dostupné z: https://doi.org/10.1007/s10773-025-05965-z.

@article{2514938,
   author = {Botur, Michal and Paseka, Jan and Smolka, Richard},
   article_number = {5},
   doi = {https://doi.org/10.1007/s10773-025-05965-z},
   keywords = {Quantum logic; Complete orthomodular lattice; Categorical logic; Dagger kernel category},
   language = {eng},
   issn = {0020-7748},
   journal = {International Journal of Theoretical Physics},
   title = {A Dagger Kernel Category of Complete Orthomodular Lattices},
   url = {https://link.springer.com/article/10.1007/s10773-025-05965-z},
   volume = {64},
   year = {2025}
}

TY  - JOUR
ID  - 2514938
AU  - Botur, Michal - Paseka, Jan - Smolka, Richard
PY  - 2025
TI  - A Dagger Kernel Category of Complete Orthomodular Lattices
JF  - International Journal of Theoretical Physics
VL  - 64
IS  - 5
SP  - 1-16
EP  - 1-16
PB  - Springer
SN  - 00207748
KW  - Quantum logic
KW  - Complete orthomodular lattice
KW  - Categorical logic
KW  - Dagger kernel category
UR  - https://link.springer.com/article/10.1007/s10773-025-05965-z
N2  - 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.
ER  -

BOTUR, Michal; Jan PASEKA a Richard SMOLKA. A Dagger Kernel Category of Complete Orthomodular Lattices. \textit{International Journal of Theoretical Physics}. Springer, 2025, roč.~64, č.~5, s.~1-16. ISSN~0020-7748. Dostupné z: https://doi.org/10.1007/s10773-025-05965-z.

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