Please use this identifier to cite or link to this item:
https://hdl.handle.net/10316/43810
Title: | On Final Coalgebras of Power-Set Functors and Saturated Trees | Authors: | Adámek, Jiří Levy, Paul B. Milius, Stefan Moss, Lawrence S. Sousa, Lurdes |
Issue Date: | 2014 | Publisher: | Springer | Project: | info:eu-repo/grantAgreement/FCT/COMPETE/132981/PT | Serial title, monograph or event: | Applied Categorical Structures | Volume: | 23 | Issue: | 4 | 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. | URI: | https://hdl.handle.net/10316/43810 | DOI: | 10.1007/s10485-014-9372-9 10.1007/s10485-014-9372-9 |
Rights: | embargoedAccess |
Appears in Collections: | I&D CMUC - Artigos em Revistas Internacionais |
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saturated_trees.pdf | 205.87 kB | Adobe PDF | View/Open |
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