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Recursive coalgebras of finitary functors

  • Jiří Adámek (a1), Dominik Lücke (a2) and Stefan Milius (a1)

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.

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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] Adámek, J. and Milius, S., Terminal coalgebras and free iterative theories. Inform. Comput. 204 (2006) 11391172.
[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] Barr, M., Terminal coalgebras in well-founded set theory. Theoret. Comput. Sci. 114 (1993) 299315.
[6] Capretta, V., Uustalu, T. and Vene, V., Recursive coalgebras from comonads. Inform. Comput. 204 (2006) 437468.
[7] Koubek, V., Set functors. Comment. Math. Univ. Carolin. 12 (1971) 175195.
[8] Lambek, J., A fixpoint theorem for complete categories. Math. Z. 103 (1968) 151161.
[9] Milius, S., Completely iterative algebras and completely iterative monads. Inform. Comput. 196 (2005) 141.
[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] Rutten, J., Universal coalgebra, a theory of systems. Theoret. Comput. Sci. 249 (2000) 380.
[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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RAIRO - Theoretical Informatics and Applications
  • ISSN: 0988-3754
  • EISSN: 1290-385X
  • URL: /core/journals/rairo-theoretical-informatics-and-applications
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