Relatively terminal coalgebras

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F12%3A10133214" target="_blank" >RIV/00216208:11320/12:10133214 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1016/j.jpaa.2012.02.026" target="_blank" >http://dx.doi.org/10.1016/j.jpaa.2012.02.026</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.jpaa.2012.02.026" target="_blank" >10.1016/j.jpaa.2012.02.026</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Relatively terminal coalgebras

Popis výsledku v původním jazyce

Dana Scott's model of lambda-calculus was based on a limit construction which started from an algebra of a suitable endofunctor F and continued by iterating F. We demonstrate that this is a special case of the concept we call coalgebra relatively terminal w.r.t. the given algebra A. This means a coalgebra together with a universal coalgebra-to-algebra morphism into A. We prove that by iterating F countably many times we obtain the relatively terminal coalgebras whenever F preserves limits of omega(op)-chains. If F is unitary, we need in general omega + omega steps. And for arbitrary accessible (=bounded) set functors we need an ordinal number of steps in general. Scott's result is captured by the fact that in a CPO-enriched category, assuming that F islocally continuous, omega steps are sufficient for algebras given by projections.

Název v anglickém jazyce

Relatively terminal coalgebras

Popis výsledku anglicky

Dana Scott's model of lambda-calculus was based on a limit construction which started from an algebra of a suitable endofunctor F and continued by iterating F. We demonstrate that this is a special case of the concept we call coalgebra relatively terminal w.r.t. the given algebra A. This means a coalgebra together with a universal coalgebra-to-algebra morphism into A. We prove that by iterating F countably many times we obtain the relatively terminal coalgebras whenever F preserves limits of omega(op)-chains. If F is unitary, we need in general omega + omega steps. And for arbitrary accessible (=bounded) set functors we need an ordinal number of steps in general. Scott's result is captured by the fact that in a CPO-enriched category, assuming that F islocally continuous, omega steps are sufficient for algebras given by projections.

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

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Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2012

Kód důvěrnosti údajů

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

Název periodika

Journal of Pure and Applied Algebra

ISSN

0022-4049

e-ISSN

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Svazek periodika

216

Číslo periodika v rámci svazku

8-9

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

9

Strana od-do

1887-1895

Kód UT WoS článku

000305670800017

EID výsledku v databázi Scopus

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