A categorical view of varieties of ordered algebras
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F22%3A00363340" target="_blank" >RIV/68407700:21230/22:00363340 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1017/S0960129521000463" target="_blank" >https://doi.org/10.1017/S0960129521000463</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1017/S0960129521000463" target="_blank" >10.1017/S0960129521000463</a>
Alternative languages
Result language
angličtina
Original language name
A categorical view of varieties of ordered algebras
Original language description
It is well known that classical varieties of Sigma-algebras correspond bijectively to finitary monads on Set. We present an analogous result for varieties of ordered Sigma-algebras, that is, categories of algebras presented by inequations between Sigma-terms. We prove that they correspond bijectively to strongly finitary monads on Pos. That is, those finitary monads which preserve reflexive coinserters. We deduce that strongly finitary monads have a coinserter presentation, analogous to the coequalizer presentation of finitary monads due to Kelly and Power. We also show that these monads are linings of finitary monads on Set. Finally, varieties presented by equations are proved to correspond to extensions of finitary monads on Set to strongly finitary monads on Pos.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GA19-00902S" target="_blank" >GA19-00902S: Injectivity and Monads in Algebra and Topology</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Mathematical Structures in Computer Science
ISSN
0960-1295
e-ISSN
1469-8072
Volume of the periodical
32
Issue of the periodical within the volume
4
Country of publishing house
GB - UNITED KINGDOM
Number of pages
25
Pages from-to
349-373
UT code for WoS article
000740897600001
EID of the result in the Scopus database
2-s2.0-85123954140