Elgot theories: A new perspective on the equational properties of iteration

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F11%3A00179252" target="_blank" >RIV/68407700:21230/11:00179252 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1017/S0960129510000496" target="_blank" >http://dx.doi.org/10.1017/S0960129510000496</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1017/S0960129510000496" target="_blank" >10.1017/S0960129510000496</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Elgot theories: A new perspective on the equational properties of iteration

Popis výsledku v původním jazyce

Bloom and Ésik's concept of iteration theory summarises all equational properties that iteration has in common applications, for example, in domain theory, where to every system of recursive equations, the least solution is assigned. This paper shows that in the coalgebraic approach to iteration, the more appropriate concept is that of a functorial iteration theory (called Elgot theory). These theories have a particularly simple axiomatisation, and all well-known examples of iteration theories are functorial. Elgot theories are proved to be monadic over the category of sets in context (or, more generally, the category of finitary endofunctors of a locally finitely presentable category). This demonstrates that functoriality is an equational property from the perspective of sets in context. In contrast, Bloom and Ésik worked in the base category of signatures rather than sets in context, and there iteration theories are monadic

Název v anglickém jazyce

Elgot theories: A new perspective on the equational properties of iteration

Popis výsledku anglicky

Bloom and Ésik's concept of iteration theory summarises all equational properties that iteration has in common applications, for example, in domain theory, where to every system of recursive equations, the least solution is assigned. This paper shows that in the coalgebraic approach to iteration, the more appropriate concept is that of a functorial iteration theory (called Elgot theory). These theories have a particularly simple axiomatisation, and all well-known examples of iteration theories are functorial. Elgot theories are proved to be monadic over the category of sets in context (or, more generally, the category of finitary endofunctors of a locally finitely presentable category). This demonstrates that functoriality is an equational property from the perspective of sets in context. In contrast, Bloom and Ésik worked in the base category of signatures rather than sets in context, and there iteration theories are monadic

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

—

Návaznosti

Z - Vyzkumny zamer (s odkazem do CEZ)

Rok uplatnění

2011

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Mathematical Structures in Computer Science

ISSN

0960-1295

e-ISSN

—

Svazek periodika

2011

Číslo periodika v rámci svazku

21

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

64

Strana od-do

417-480

Kód UT WoS článku

000289006300008

EID výsledku v databázi Scopus

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