Fixed points of functors

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F18%3A00322018" target="_blank" >RIV/68407700:21230/18:00322018 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1016/j.jlamp.2017.11.003" target="_blank" >http://dx.doi.org/10.1016/j.jlamp.2017.11.003</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.jlamp.2017.11.003" target="_blank" >10.1016/j.jlamp.2017.11.003</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Fixed points of functors

Popis výsledku v původním jazyce

This is a survey on fixed points of endofunctors, including initial algebras and terminal coalgebras. We also consider the rational fixed point, a canonical domain of behavior for finitely presentable systems. In addition to the basic existence theorems for fixed points, several new results are presented. For example, the Smyth-Plotkin theorem that locally continuous endofunctors of DCPO have terminal coalgebras is derived from a new result stating that every locally monotone endofunctor with a fixed point has a terminal coalgebra. We introduce bounded endofunctors on abstract categories and prove that they have terminal coalgebras. We study well-founded coalgebras and prove that for set functors, the largest well-founded coalgebra of every fixed point is the initial algebra. Another new result concerns mixed fixed points: initial algebras and terminal coalgebras of a parametrized accessible functor always form accessible functors. (C) 2017 Elsevier Inc. All rights reserved.

Název v anglickém jazyce

Fixed points of functors

Popis výsledku anglicky

This is a survey on fixed points of endofunctors, including initial algebras and terminal coalgebras. We also consider the rational fixed point, a canonical domain of behavior for finitely presentable systems. In addition to the basic existence theorems for fixed points, several new results are presented. For example, the Smyth-Plotkin theorem that locally continuous endofunctors of DCPO have terminal coalgebras is derived from a new result stating that every locally monotone endofunctor with a fixed point has a terminal coalgebra. We introduce bounded endofunctors on abstract categories and prove that they have terminal coalgebras. We study well-founded coalgebras and prove that for set functors, the largest well-founded coalgebra of every fixed point is the initial algebra. Another new result concerns mixed fixed points: initial algebras and terminal coalgebras of a parametrized accessible functor always form accessible functors. (C) 2017 Elsevier Inc. 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

2018

Kód důvěrnosti údajů

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

Název periodika

Journal of Logical and Algebraic Methods in Programming

ISSN

2352-2208

e-ISSN

—

Svazek periodika

95

Číslo periodika v rámci svazku

FEB

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

41

Strana od-do

41-81

Kód UT WoS článku

000425079300003

EID výsledku v databázi Scopus

2-s2.0-85043482597