Fixed points of functors

Result code in 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>
Result on the web
<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>

Result language
angličtina
Original language name
Fixed points of functors
Original language description
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.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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