Final coalgebras in accessible categories

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F11%3A00181887" target="_blank" >RIV/68407700:21230/11:00181887 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1017/S0960129511000351" target="_blank" >http://dx.doi.org/10.1017/S0960129511000351</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1017/S0960129511000351" target="_blank" >10.1017/S0960129511000351</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Final coalgebras in accessible categories

Popis výsledku v původním jazyce

We propose a construction of the final coalgebra for a finitary endofunctor of a finitely accessible category and study conditions under which this construction is available. Our conditions always apply when the accessible category is cocomplete, and isthus a locally finitely presentable (l.f.p.) category, and we give an explicit and uniform construction of the final coalgebra in this case. On the other hand, our results also apply to some interesting examples of final coalgebras beyond the realm of l.f.p. categories. In particular, we construct the final coalgebra for every finitary endofunctor on the category of linear orders, and analyse Freyd's coalgebraic characterisation of the closed unit as an instance of this construction. We use and extend results of Tom Leinster, developed for his study of self-similar objects in topology, relying heavily on his formalism of modules (corresponding to endofunctors) and complexes for a module.

Název v anglickém jazyce

Final coalgebras in accessible categories

Popis výsledku anglicky

We propose a construction of the final coalgebra for a finitary endofunctor of a finitely accessible category and study conditions under which this construction is available. Our conditions always apply when the accessible category is cocomplete, and isthus a locally finitely presentable (l.f.p.) category, and we give an explicit and uniform construction of the final coalgebra in this case. On the other hand, our results also apply to some interesting examples of final coalgebras beyond the realm of l.f.p. categories. In particular, we construct the final coalgebra for every finitary endofunctor on the category of linear orders, and analyse Freyd's coalgebraic characterisation of the closed unit as an instance of this construction. We use and extend results of Tom Leinster, developed for his study of self-similar objects in topology, relying heavily on his formalism of modules (corresponding to endofunctors) and complexes for a module.

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

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Svazek periodika

21

Číslo periodika v rámci svazku

5

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

42

Strana od-do

1067-1108

Kód UT WoS článku

000295315000004

EID výsledku v databázi Scopus

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