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Recursive coalgebras of finitary functors

Published online by Cambridge University Press:  17 August 2007

Jiří Adámek
Affiliation:
Technical University of Braunschweig, Institute of Theoretical Computer Science, Braunschweig, Germany; adamek@iti.cs.tu-bs.de; milius@iti.cs.tu-bs.de
Dominik Lücke
Affiliation:
Department of Computer Science, University of Bremen, PO Box 330440, 28334 Bremen, Germany; luecke@tzi.de
Stefan Milius
Affiliation:
Technical University of Braunschweig, Institute of Theoretical Computer Science, Braunschweig, Germany; adamek@iti.cs.tu-bs.de; milius@iti.cs.tu-bs.de
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Abstract

For finitary set functors preserving inverse images, recursive coalgebras A of Paul Taylor are proved to be precisely those for which the system described by A always halts in finitely many steps.

Type
Research Article
Copyright
© EDP Sciences, 2007

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References

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J. Adámek, D. Lücke and S. Milius, Recursive coalgebras of finitary functors, in CALCO-jnr 2005 CALCO Young Researchers Workshop Selected Papers, edited by P. Mosses, J. Power and M. Seisenberger, Report Series, University of Swansea, 1–14.
Barr, M., Terminal coalgebras in well-founded set theory. Theoret. Comput. Sci. 114 (1993) 299315. CrossRef
Capretta, V., Uustalu, T. and Vene, V., Recursive coalgebras from comonads. Inform. Comput. 204 (2006) 437468. CrossRef
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Lambek, J., A fixpoint theorem for complete categories. Math. Z. 103 (1968) 151161. CrossRef
Milius, S., Completely iterative algebras and completely iterative monads. Inform. Comput. 196 (2005) 141. CrossRef
R. Montague, Well-founded relations; generalizations of principles of induction and recursion (abstract). Bull. Amer. Math. Soc. 61 (1955) 442.
G. Osius, Categorical set theory: a characterization of the category of sets. J. Pure Appl. Algebra  4 (1974) 79–119. CrossRef
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P. Taylor, Practical Foundations of Mathematics. Cambridge University Press (1999).
V. Trnková, On a descriptive classification of set-functors I. Comment. Math. Univ. Carolin. 12 (1971) 143–174.

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