Relatively terminal coalgebras

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F12%3A10133214" target="_blank" >RIV/00216208:11320/12:10133214 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.jpaa.2012.02.026" target="_blank" >http://dx.doi.org/10.1016/j.jpaa.2012.02.026</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jpaa.2012.02.026" target="_blank" >10.1016/j.jpaa.2012.02.026</a>

Result language
angličtina
Original language name
Relatively terminal coalgebras
Original language description
Dana Scott's model of lambda-calculus was based on a limit construction which started from an algebra of a suitable endofunctor F and continued by iterating F. We demonstrate that this is a special case of the concept we call coalgebra relatively terminal w.r.t. the given algebra A. This means a coalgebra together with a universal coalgebra-to-algebra morphism into A. We prove that by iterating F countably many times we obtain the relatively terminal coalgebras whenever F preserves limits of omega(op)-chains. If F is unitary, we need in general omega + omega steps. And for arbitrary accessible (=bounded) set functors we need an ordinal number of steps in general. Scott's result is captured by the fact that in a CPO-enriched category, assuming that F islocally continuous, omega steps are sufficient for algebras given by projections.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2012
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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