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

Abstract

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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.

How to cite

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Adámek, 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

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  1. 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.  
  2. J. Adámek and S. Milius, Terminal coalgebras and free iterative theories. Inform. Comput.204 (2006) 1139–1172.  
  3. J. Adámek and V. Trnková, Automata and Algebras in Categories. Kluwer Academic Publishers (1990).  
  4. 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.  
  5. M. Barr, Terminal coalgebras in well-founded set theory. Theoret. Comput. Sci.114 (1993) 299–315.  
  6. V. Capretta, T. Uustalu and V. Vene, Recursive coalgebras from comonads. Inform. Comput.204 (2006) 437–468.  
  7. V. Koubek, Set functors. Comment. Math. Univ. Carolin.12 (1971) 175–195.  
  8. J. Lambek, A fixpoint theorem for complete categories. Math. Z.103 (1968) 151–161.  
  9. S. Milius, Completely iterative algebras and completely iterative monads. Inform. Comput.196 (2005) 1–41.  
  10. R. Montague, Well-founded relations; generalizations of principles of induction and recursion (abstract). Bull. Amer. Math. Soc.61 (1955) 442.  
  11. G. Osius, Categorical set theory: a characterization of the category of sets. J. Pure Appl. Algebra 4 (1974) 79–119.  
  12. J. Rutten, Universal coalgebra, a theory of systems. Theoret. Comput. Sci.249 (2000) 3–80.  
  13. P. Taylor, Practical Foundations of Mathematics. Cambridge University Press (1999).  
  14. V. Trnková, On a descriptive classification of set-functors I. Comment. Math. Univ. Carolin.12 (1971) 143–174.  

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