On terminal coalgebras derived from initial algebras

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F19%3A00338247" target="_blank" >RIV/68407700:21230/19:00338247 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.4230/LIPIcs.CALCO.2019.12" target="_blank" >https://doi.org/10.4230/LIPIcs.CALCO.2019.12</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.4230/LIPIcs.CALCO.2019.12" target="_blank" >10.4230/LIPIcs.CALCO.2019.12</a>

Result language
angličtina
Original language name
On terminal coalgebras derived from initial algebras
Original language description
A number of important set functors have countable initial algebras, but terminal coalgebras areuncountable or even non-existent. We prove that the countable cardinality is an anomaly: every setfunctor with an initial algebra of a finite or uncountable regular cardinality has a terminal coalgebraof the same cardinality.We also present a number of categories that are algebraically complete and cocomplete, i.e.,every endofunctor has an initial algebra and a terminal coalgebra.Finally, for finitary set functors we prove that the initial algebraμFand terminal coalgebraνFcarry a canonical ultrametric with the joint Cauchy completion. And the algebra structure ofμFdetermines, by extending its inverse continuously, the coalgebra structure ofνF.
Czech name
—
Czech description
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Project
<a href="/en/project/GA19-00902S" target="_blank" >GA19-00902S: Injectivity and Monads in Algebra and Topology</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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