Iterative Algebras at Work
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F06%3A03125206" target="_blank" >RIV/68407700:21230/06:03125206 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Alternative languages
Result language
angličtina
Original language name
Iterative Algebras at Work
Original language description
Iterative theories, which were introduced by Calvin Elgot, formalise potentially infinite computations as unique solutions of recursive equations. One of the main results of Elgot and his coauthors is a description of a free iterative theory as the theory of all rational trees. Their algebraic proof of this fact is extremely complicated. In our paper we show that by starting with iterative algebras, that is, algebras admitting a unique solution of all systems of flat recursive equations, a free iterative theory is obtained as the theory of free iterative algebras. The (coalgebraic) proof we present is dramatically simpler than the original algebraic one. Despite this, our result is much more general: we describe a free iterative theory on any finitaryendofunctor of every locally presentable category.
Czech name
Iterativni algebry v plne sile
Czech description
Iterativni teorie, zavedene Calvinem Elgotem, formalizuji potencionalne nekonecne vypocty jako jednoznacna reseni rekursivnich rovnic. Jednim z hlavnich vysledku Elgota a jeho spoluautoru byl popis volne iterativni teorie jako teorie racionalnich stromu.Algebraicky dukaz tohoto faktu je velmi slozity. V nasi praci ukazujeme, ze pokud zacneme s iterativnimi algebrami, obdrzime volnou iterativni teorii jako teorii volnych iterativnich algeber. Nas koalgebraicky dukaz je znacne jendodussi nez puvodni algebraicky. Navic je nas vysledek obecnejsi: popisujeme volnou iterativni teorii pro libovolny finitarni endofunktor na libovolne lokalne konecne presentovane kategorii
Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
<a href="/en/project/GA201%2F06%2F0664" target="_blank" >GA201/06/0664: Categorical methods of the theory of structures</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2006
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
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Volume of the periodical
2006
Issue of the periodical within the volume
16
Country of publishing house
GB - UNITED KINGDOM
Number of pages
47
Pages from-to
1085-1131
UT code for WoS article
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EID of the result in the Scopus database
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