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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

  • Czech description

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