Which categories are varieties of quantitative algebras?

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F25%3A00389440" target="_blank" >RIV/68407700:21230/25:00389440 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1016/j.jpaa.2025.108139" target="_blank" >https://doi.org/10.1016/j.jpaa.2025.108139</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.jpaa.2025.108139" target="_blank" >10.1016/j.jpaa.2025.108139</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Which categories are varieties of quantitative algebras?

Popis výsledku v původním jazyce

Classical varieties were characterized by Lawvere as the categories with effective congruences and a varietal generator: an abstractly finite, regular generator which is regularly projective (its hom-functor preserves regular epimorphisms). We characterize varieties of quantitative algebras of Mardare, Panangaden and Plotkin analogously as metric-enriched categories. We introduce the concept of a subcongruence (a metric-enriched analogue of a congruence) and the corresponding subregular epimorphisms, obtained via colimits of subcongruences. Varieties of quantitative algebras are precisely the metric-enriched categories with effective subcongruences and a subvarietal generator: an abstractly finite, subregular generator which is subregularly projective (its hom-functor preserves subregular epimorphisms). (c) 2025 Published by Elsevier B.V.

Název v anglickém jazyce

Which categories are varieties of quantitative algebras?

Popis výsledku anglicky

Classical varieties were characterized by Lawvere as the categories with effective congruences and a varietal generator: an abstractly finite, regular generator which is regularly projective (its hom-functor preserves regular epimorphisms). We characterize varieties of quantitative algebras of Mardare, Panangaden and Plotkin analogously as metric-enriched categories. We introduce the concept of a subcongruence (a metric-enriched analogue of a congruence) and the corresponding subregular epimorphisms, obtained via colimits of subcongruences. Varieties of quantitative algebras are precisely the metric-enriched categories with effective subcongruences and a subvarietal generator: an abstractly finite, subregular generator which is subregularly projective (its hom-functor preserves subregular epimorphisms). (c) 2025 Published by Elsevier B.V.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA22-02964S" target="_blank" >GA22-02964S: Obohacené kategorie a jejich aplikace</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2025

Kód důvěrnosti údajů

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

Název periodika

Journal of Pure and Applied Algebra

ISSN

0022-4049

e-ISSN

1873-1376

Svazek periodika

229

Číslo periodika v rámci svazku

12

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

35

Strana od-do

—

Kód UT WoS článku

001638492400001

EID výsledku v databázi Scopus

2-s2.0-105024116857