Approximate coalgebra homomorphisms and approximate solutions

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F20%3A00346315" target="_blank" >RIV/68407700:21230/20:00346315 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1007/978-3-030-57201-3_2" target="_blank" >https://doi.org/10.1007/978-3-030-57201-3_2</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/978-3-030-57201-3_2" target="_blank" >10.1007/978-3-030-57201-3_2</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Approximate coalgebra homomorphisms and approximate solutions

Popis výsledku v původním jazyce

Terminal coalgebras ν F of finitary endofunctors F on categories called strongly lfp are proved to carry a canonical ultrametric on their underlying sets. The subspace formed by the initial algebra μ F has the property that for every coalgebra A we obtain its unique homomorphism into ν F as a limit of a Cauchy sequence of morphisms into μ F called approximate homomorphisms. The concept of a strongly lfp category includes categories of sets, posets, vector spaces, boolean algebras, and many others. For the free completely iterative algebra Ψ B on a pointed object B we analogously present a canonical ultrametric on its underlying set. The subspace formed by the free algebra φ B on B has the property that for every recursive equation in Ψ B we obtain the unique solution as a limit of a Cauchy sequence of morphisms into φ B called approximate solutions. A completely analogous result holds for the free iterative algebra RB on B.

Název v anglickém jazyce

Approximate coalgebra homomorphisms and approximate solutions

Popis výsledku anglicky

Terminal coalgebras ν F of finitary endofunctors F on categories called strongly lfp are proved to carry a canonical ultrametric on their underlying sets. The subspace formed by the initial algebra μ F has the property that for every coalgebra A we obtain its unique homomorphism into ν F as a limit of a Cauchy sequence of morphisms into μ F called approximate homomorphisms. The concept of a strongly lfp category includes categories of sets, posets, vector spaces, boolean algebras, and many others. For the free completely iterative algebra Ψ B on a pointed object B we analogously present a canonical ultrametric on its underlying set. The subspace formed by the free algebra φ B on B has the property that for every recursive equation in Ψ B we obtain the unique solution as a limit of a Cauchy sequence of morphisms into φ B called approximate solutions. A completely analogous result holds for the free iterative algebra RB on B.

Druh

D - Stať ve sborníku

CEP obor

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OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA19-00902S" target="_blank" >GA19-00902S: Injektivita a monády v algebře a topologii</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2020

Kód důvěrnosti údajů

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

Název statě ve sborníku

Coalgebraic Methods in Computer Science

ISBN

978-3-030-57200-6

ISSN

0302-9743

e-ISSN

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Počet stran výsledku

21

Strana od-do

11-31

Název nakladatele

Springer International Publishing

Místo vydání

Cham

Místo konání akce

Dublin

Datum konání akce

25. 4. 2021

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

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