Which categories are varieties of quantitative algebras?

Result code in 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>

Result on the web

<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>

Result language

angličtina

Original language name

Which categories are varieties of quantitative algebras?

Original language description

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.

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

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OECD FORD branch

10101 - Pure mathematics

Project

<a href="/en/project/GA22-02964S" target="_blank" >GA22-02964S: Enriched categories and their applications</a><br>

Continuities

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

Publication year

2025

Confidentiality

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

Name of the periodical

Journal of Pure and Applied Algebra

ISSN

0022-4049

e-ISSN

1873-1376

Volume of the periodical

229

Issue of the periodical within the volume

12

Country of publishing house

NL - THE KINGDOM OF THE NETHERLANDS

Number of pages

35

Pages from-to

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UT code for WoS article

001638492400001

EID of the result in the Scopus database

2-s2.0-105024116857