Varieties of Qantitative Algebras and Their Monads

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F22%3A00363394" target="_blank" >RIV/68407700:21230/22:00363394 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1145/3531130.3532405" target="_blank" >https://doi.org/10.1145/3531130.3532405</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1145/3531130.3532405" target="_blank" >10.1145/3531130.3532405</a>

Result language
angličtina
Original language name
Varieties of Qantitative Algebras and Their Monads
Original language description
Quantitative Σ-algebras, where Σ is a signature with countable arities, are Σ-algebras equipped with a metric making all operations nonexpanding. They have been studied by Mardare, Panangaden and Plotkin who also introduced c-basic quantitative equations for regular cardinals c. Categories of quantitative algebras that can be presented by such equations for c = ℵ1 are called ω1-varieties. We prove that they are precisely the monadic categories , where is a countably basic monad on the category of metric spaces. For Σ finitary one speaks about ω-varieties for c = ℵ0. If all spaces used are restricted to UMet, the category of ultrametric spaces, then ω-varieties are precisely the monadic categories , where is a finitely basic monad.
Czech name
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Czech description
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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
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Article name in the collection
Proceedings of the 37th Annual ACM/IEEE Symposium on Logic in Computer Science
ISBN
978-1-4503-9351-5
ISSN
1043-6871
e-ISSN
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Number of pages
10
Pages from-to
1-10
Publisher name
Association for Computing Machinery
Place of publication
New York
Event location
Haifa
Event date
Aug 2, 2022
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
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