On functors preserving coproducts and algebras with iterativity

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F19%3A00332920" target="_blank" >RIV/68407700:21230/19:00332920 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1016/j.tcs.2019.01.018" target="_blank" >https://doi.org/10.1016/j.tcs.2019.01.018</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.tcs.2019.01.018" target="_blank" >10.1016/j.tcs.2019.01.018</a>

Jazyk výsledku

angličtina

Název v původním jazyce

On functors preserving coproducts and algebras with iterativity

Popis výsledku v původním jazyce

An algebra for a functor H is called completely iterative (cia, for short) if every flat recursive equation in it has a unique solution. Every cia is corecursive, i.e., it admits a unique coalgebra-to-algebra morphism from every coalgebra. If the converse also holds, H is called a cia functor. We prove that whenever the base category is hyper-extensive (i.e. countable coproducts are 'well-behaved') and H preserves countable coproducts, then H is a cia functor. Surprisingly few cia functors exist among standard finitary set functors: in fact, the only ones are those preserving coproducts; they are given by X bar right arrow W x (-) + Y for some sets W and Y. (C) 2019 Elsevier B.V. All rights reserved.

Název v anglickém jazyce

On functors preserving coproducts and algebras with iterativity

Popis výsledku anglicky

An algebra for a functor H is called completely iterative (cia, for short) if every flat recursive equation in it has a unique solution. Every cia is corecursive, i.e., it admits a unique coalgebra-to-algebra morphism from every coalgebra. If the converse also holds, H is called a cia functor. We prove that whenever the base category is hyper-extensive (i.e. countable coproducts are 'well-behaved') and H preserves countable coproducts, then H is a cia functor. Surprisingly few cia functors exist among standard finitary set functors: in fact, the only ones are those preserving coproducts; they are given by X bar right arrow W x (-) + Y for some sets W and Y. (C) 2019 Elsevier B.V. All rights reserved.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2019

Kód důvěrnosti údajů

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

Název periodika

Theoretical Computer Science

ISSN

0304-3975

e-ISSN

1879-2294

Svazek periodika

763

Číslo periodika v rámci svazku

Apr

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

22

Strana od-do

66-87

Kód UT WoS článku

000460854400004

EID výsledku v databázi Scopus

2-s2.0-85060763567