On Kripke, Vietoris and Hausdorff Polynomial Functors

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F23%3A00373106" target="_blank" >RIV/68407700:21230/23:00373106 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.4230/LIPIcs.CALCO.2023.21" target="_blank" >https://doi.org/10.4230/LIPIcs.CALCO.2023.21</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.4230/LIPIcs.CALCO.2023.21" target="_blank" >10.4230/LIPIcs.CALCO.2023.21</a>

Result language
angličtina
Original language name
On Kripke, Vietoris and Hausdorff Polynomial Functors
Original language description
The Vietoris space of compact subsets of a given Hausdorff space yields an endofunctor V on the category of Hausdorff spaces. Vietoris polynomial endofunctors on that category are built from V, the identity and constant functors by forming products, coproducts and compositions. These functors are known to have terminal coalgebras and we deduce that they also have initial algebras. We present an analogous class of endofunctors on the category of extended metric spaces, using in lieu of V the Hausdorff functor H. We prove that the ensuing Hausdorff polynomial functors have terminal coalgebras and initial algebras. Whereas the canonical constructions of terminal coalgebras for Vietoris polynomial functors take ω steps, one needs ω + ω steps in general for Hausdorff ones. We also give a new proof that the closed set functor on metric spaces has no fixed points.
Czech name
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Czech description
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Project
<a href="/en/project/GA22-02964S" target="_blank" >GA22-02964S: Enriched categories and their applications</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Article name in the collection
10th Conference on Algebra and Coalgebra in Computer Science (CALCO 2023)
ISBN
978-3-95977-287-7
ISSN
1868-8969
e-ISSN
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Number of pages
20
Pages from-to
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Publisher name
Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik
Place of publication
Dagstuhl
Event location
Bloomington
Event date
Jun 19, 2023
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
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