Home Publications Research Grants Inventions & Patents Awards Additional Research Activities Faculties & Institutions Research Areas

On Final Coalgebras of Power-Set Functors and Saturated Trees

Adámek J, Levy P, Milius S, Moss L, Sousa L (2015)

---

Publication Type: Journal article

Publication year: 2015

Journal

Publisher: Springer Verlag (Germany)

Book Volume: 23

Pages Range: 609-641

Journal Issue: 4

URI: http://www.stefan-milius.eu

DOI: 10.1007/s10485-014-9372-9

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 Pλ, 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 ℳf 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. © 2014 Springer Science+Business Media Dordrecht.

Authors with CRIS profile

Involved external institutions

How to cite

APA:

Adámek, J., Levy, P., Milius, S., Moss, L., & Sousa, L. (2015). On Final Coalgebras of Power-Set Functors and Saturated Trees. Applied Categorical Structures, 23(4), 609-641. https://dx.doi.org/10.1007/s10485-014-9372-9

MLA:

Adámek, Jiří, et al. "On Final Coalgebras of Power-Set Functors and Saturated Trees." Applied Categorical Structures 23.4 (2015): 609-641.

BibTeX: Download