On functors preserving coproducts and algebras with iterativity

Result code in 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>
Result on the web
<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>

Result language
angličtina
Original language name
On functors preserving coproducts and algebras with iterativity
Original language description
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.
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
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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