The Category of ω-Effect Algebras: Tensor Product and ω-Completion

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F25%3A73627618" target="_blank" >RIV/61989592:15310/25:73627618 - isvavai.cz</a>

Výsledek na webu

<a href="https://link.springer.com/article/10.1007/s11083-024-09680-y" target="_blank" >https://link.springer.com/article/10.1007/s11083-024-09680-y</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s11083-024-09680-y" target="_blank" >10.1007/s11083-024-09680-y</a>

Jazyk výsledku

angličtina

Název v původním jazyce

The Category of ω-Effect Algebras: Tensor Product and ω-Completion

Popis výsledku v původním jazyce

Effect algebras are certain ordered structures that serve as a general framework for studying the algebraic semantics of quantum logic. We study effect algebras which obtain suprema of countable monotone sequences – so-called ω-effect algebras. This assumption is necessary to capture basic (non-discrete) probabilistic concepts. We establish a free ω-completion of effect algebras (i.e., a left adjoint to the functor that forgets the existence of ω-suprema) and the existence of a tensor product in the category of ω-effect algebras. These results are obtained by means of so-called test spaces. Test spaces form a category that contains effect algebras as a reflective subcategory, but provides more space for constructions.

Název v anglickém jazyce

The Category of ω-Effect Algebras: Tensor Product and ω-Completion

Popis výsledku anglicky

Effect algebras are certain ordered structures that serve as a general framework for studying the algebraic semantics of quantum logic. We study effect algebras which obtain suprema of countable monotone sequences – so-called ω-effect algebras. This assumption is necessary to capture basic (non-discrete) probabilistic concepts. We establish a free ω-completion of effect algebras (i.e., a left adjoint to the functor that forgets the existence of ω-suprema) and the existence of a tensor product in the category of ω-effect algebras. These results are obtained by means of so-called test spaces. Test spaces form a category that contains effect algebras as a reflective subcategory, but provides more space for constructions.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2025

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

ORDER-A JOURNAL ON THE THEORY OF ORDERED SETS AND ITS APPLICATIONS

ISSN

0167-8094

e-ISSN

1572-9273

Svazek periodika

42

Číslo periodika v rámci svazku

AUG

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

18

Strana od-do

253-270

Kód UT WoS článku

001303247100001

EID výsledku v databázi Scopus

2-s2.0-85202678299