Fixed Points of Set Functors: How Many Iterations are Needed?

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F16%3A10329041" target="_blank" >RIV/00216208:11320/16:10329041 - isvavai.cz</a>

Alternative codes found

RIV/68407700:21230/16:00302998

Result on the web

<a href="http://dx.doi.org/10.1007/s10485-016-9451-1" target="_blank" >http://dx.doi.org/10.1007/s10485-016-9451-1</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s10485-016-9451-1" target="_blank" >10.1007/s10485-016-9451-1</a>

Result language

angličtina

Original language name

Fixed Points of Set Functors: How Many Iterations are Needed?

Original language description

The initial algebra for a set functor can be constructed iteratively via a well-known transfinite chain, which converges after a regular infinite cardinal number of steps or at most three steps. We extend this result to the analogous construction of relatively initial algebras. For the dual construction of the terminal coalgebra Worrell proved that if a set functor is alpha-accessible, then convergence takes at most alpha + alpha steps. But until now an example demonstrating that fewer steps may be insufficient was missing. We prove that the functor of all alpha-small filters is such an example. We further prove that for beta aecurrency sign alpha the functor of all alpha-small beta-generated filters requires precisely alpha + beta steps and that a certain modified power-set functor requires precisely alpha steps. We also present an example showing that whether a terminal coalgebra exists at all does not depend solely on the object mapping of the given set functor. (This contrasts with the fact that existence of an initial algebra is equivalent to existence of a mere fixed point.).

Czech name

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Czech description

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Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

IN - Informatics

OECD FORD branch

—

Project

—

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2016

Confidentiality

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

Name of the periodical

Applied Categorical Structures

ISSN

0927-2852

e-ISSN

—

Volume of the periodical

24

Issue of the periodical within the volume

5

Country of publishing house

NL - THE KINGDOM OF THE NETHERLANDS

Number of pages

13

Pages from-to

649-661

UT code for WoS article

000383603000015

EID of the result in the Scopus database

2-s2.0-84983542777