Final coalgebras in accessible categories

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F11%3A00181887" target="_blank" >RIV/68407700:21230/11:00181887 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1017/S0960129511000351" target="_blank" >http://dx.doi.org/10.1017/S0960129511000351</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1017/S0960129511000351" target="_blank" >10.1017/S0960129511000351</a>

Result language
angličtina
Original language name
Final coalgebras in accessible categories
Original language description
We propose a construction of the final coalgebra for a finitary endofunctor of a finitely accessible category and study conditions under which this construction is available. Our conditions always apply when the accessible category is cocomplete, and isthus a locally finitely presentable (l.f.p.) category, and we give an explicit and uniform construction of the final coalgebra in this case. On the other hand, our results also apply to some interesting examples of final coalgebras beyond the realm of l.f.p. categories. In particular, we construct the final coalgebra for every finitary endofunctor on the category of linear orders, and analyse Freyd's coalgebraic characterisation of the closed unit as an instance of this construction. We use and extend results of Tom Leinster, developed for his study of self-similar objects in topology, relying heavily on his formalism of modules (corresponding to endofunctors) and complexes for a module.
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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Publication year
2011
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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