Please use this identifier to cite or link to this item:
https://hdl.handle.net/10316/43810
DC Field | Value | Language |
---|---|---|
dc.contributor.author | Adámek, Jiří | - |
dc.contributor.author | Levy, Paul B. | - |
dc.contributor.author | Milius, Stefan | - |
dc.contributor.author | Moss, Lawrence S. | - |
dc.contributor.author | Sousa, Lurdes | - |
dc.date.accessioned | 2017-10-10T08:47:18Z | - |
dc.date.issued | 2014 | - |
dc.identifier.uri | https://hdl.handle.net/10316/43810 | - |
dc.description.abstract | The final coalgebra for the finite power-set functor was described by Worrell who also proved that the final chain converges in ω+ω steps. We describe the step ω as the set of saturated trees, a concept equivalent to the modally saturated trees introduced by K. Fine in the 1970s in his study of modal logic. And for the bounded power-set functors P_λ, where λ is an infinite regular cardinal, we prove that the construction needs precisely λ+ω steps. We also generalize Worrell’s result to M-labeled trees for a commutative monoid M, yielding a final coalgebra for the corresponding functor ℳ_f studied by H.-P. Gumm and T. Schröder. We describe the final chain of the power-set functor by introducing the concept of i-saturated tree for all ordinals i, and then prove that for i of cofinality ω, the i-th step in the final chain consists of all i-saturated, strongly extensional trees. | por |
dc.language.iso | eng | por |
dc.publisher | Springer | por |
dc.relation | info:eu-repo/grantAgreement/FCT/COMPETE/132981/PT | por |
dc.rights | embargoedAccess | - |
dc.title | On Final Coalgebras of Power-Set Functors and Saturated Trees | por |
dc.type | article | - |
degois.publication.firstPage | 609 | por |
degois.publication.lastPage | 641 | por |
degois.publication.issue | 4 | por |
degois.publication.title | Applied Categorical Structures | por |
dc.relation.publisherversion | https://link.springer.com/article/10.1007/s10485-014-9372-9 | por |
dc.peerreviewed | yes | por |
dc.identifier.doi | 10.1007/s10485-014-9372-9 | por |
dc.identifier.doi | 10.1007/s10485-014-9372-9 | - |
degois.publication.volume | 23 | por |
dc.date.embargo | 2018-10-10T08:47:18Z | - |
item.languageiso639-1 | en | - |
item.grantfulltext | open | - |
item.fulltext | Com Texto completo | - |
item.openairecristype | http://purl.org/coar/resource_type/c_18cf | - |
item.openairetype | article | - |
item.cerifentitytype | Publications | - |
crisitem.author.orcid | 0000-0003-0100-1673 | - |
Appears in Collections: | I&D CMUC - Artigos em Revistas Internacionais |
Files in This Item:
File | Description | Size | Format | |
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saturated_trees.pdf | 205.87 kB | Adobe PDF | View/Open |
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