CATEGORIES WHICH ARE VARIETIES OF CLASSICAL OR ORDERED ALGEBRAS

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F25%3A00389439" target="_blank" >RIV/68407700:21230/25:00389439 - isvavai.cz</a>
Result on the web
<a href="http://www.tac.mta.ca/tac/volumes/43/3/43-03.pdf" target="_blank" >http://www.tac.mta.ca/tac/volumes/43/3/43-03.pdf</a>
DOI - Digital Object Identifier
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Result language
angličtina
Original language name
CATEGORIES WHICH ARE VARIETIES OF CLASSICAL OR ORDERED ALGEBRAS
Original language description
Following ideas of Lawvere and Linton we prove that classical varieties are precisely the exact categories with a varietal generator. This means a strong generator which is abstractly finite and regularly projective. An analogous characterization of varieties of ordered algebras is also presented. We work with order-enriched categories, and introduce the concept of sub congruence (corresponding to congruence in ordinary categories): it is a relation which is order-reflexive and transitive. Varieties of ordered algebras are precisely the categories with effective sub congruences and a subvarietal generator. This means a strong generator which is abstractly finite and subregularly projective.
Czech name
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Czech description
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Type
J<sub>imp</sub> - 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

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