# Recursive coalgebras of finitary functors

Jiří Adámek; Dominik Lücke; Stefan Milius

RAIRO - Theoretical Informatics and Applications (2007)

- Volume: 41, Issue: 4, page 447-462
- ISSN: 0988-3754

## Access Full Article

top## Abstract

top## How to cite

topAdámek, Jiří, Lücke, Dominik, and Milius, Stefan. "Recursive coalgebras of finitary functors." RAIRO - Theoretical Informatics and Applications 41.4 (2007): 447-462. <http://eudml.org/doc/250019>.

@article{Adámek2007,

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.
},

author = {Adámek, Jiří, Lücke, Dominik, Milius, Stefan},

journal = {RAIRO - Theoretical Informatics and Applications},

keywords = {Recursive coalgebra; coalgebra; definition by recursivity; recursive coalgebra},

language = {eng},

month = {8},

number = {4},

pages = {447-462},

publisher = {EDP Sciences},

title = {Recursive coalgebras of finitary functors},

url = {http://eudml.org/doc/250019},

volume = {41},

year = {2007},

}

TY - JOUR

AU - Adámek, Jiří

AU - Lücke, Dominik

AU - Milius, Stefan

TI - Recursive coalgebras of finitary functors

JO - RAIRO - Theoretical Informatics and Applications

DA - 2007/8//

PB - EDP Sciences

VL - 41

IS - 4

SP - 447

EP - 462

AB -
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.

LA - eng

KW - Recursive coalgebra; coalgebra; definition by recursivity; recursive coalgebra

UR - http://eudml.org/doc/250019

ER -

## References

top- P. Aczel and N. Mendler, A Final Coalgebra Theorem, Proceedings Category Theory and Computer Science, edited by D.H. Pitt et al.Lect. Notes Comput. Sci. (1989) 357–365.
- J. Adámek and S. Milius, Terminal coalgebras and free iterative theories. Inform. Comput.204 (2006) 1139–1172.
- J. Adámek and V. Trnková, Automata and Algebras in Categories. Kluwer Academic Publishers (1990).
- 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.
- M. Barr, Terminal coalgebras in well-founded set theory. Theoret. Comput. Sci.114 (1993) 299–315.
- V. Capretta, T. Uustalu and V. Vene, Recursive coalgebras from comonads. Inform. Comput.204 (2006) 437–468.
- V. Koubek, Set functors. Comment. Math. Univ. Carolin.12 (1971) 175–195.
- J. Lambek, A fixpoint theorem for complete categories. Math. Z.103 (1968) 151–161.
- S. Milius, Completely iterative algebras and completely iterative monads. Inform. Comput.196 (2005) 1–41.
- 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.
- J. Rutten, Universal coalgebra, a theory of systems. Theoret. Comput. Sci.249 (2000) 3–80.
- 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.

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.