Recursive coalgebras of finitary functors
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 41 (2007) no. 4, pp. 447-462.

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.

DOI : 10.1051/ita:2007028
Classification : 18A25, 08C05, 68R65
Keywords: recursive coalgebra, coalgebra, definition by recursivity
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Adámek, Jiří; Lücke, Dominik; Milius, Stefan. Recursive coalgebras of finitary functors. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 41 (2007) no. 4, pp. 447-462. doi : 10.1051/ita:2007028. https://www.numdam.org/articles/10.1051/ita:2007028/

[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. | Zbl

[3] J. Adámek and V. Trnková, Automata and Algebras in Categories. Kluwer Academic Publishers (1990). | MR | Zbl

[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. | Zbl

[6] V. Capretta, T. Uustalu and V. Vene, Recursive coalgebras from comonads. Inform. Comput. 204 (2006) 437-468. | Zbl

[7] V. Koubek, Set functors. Comment. Math. Univ. Carolin. 12 (1971) 175-195. | Zbl

[8] J. Lambek, A fixpoint theorem for complete categories. Math. Z. 103 (1968) 151-161. | Zbl

[9] S. Milius, Completely iterative algebras and completely iterative monads. Inform. Comput. 196 (2005) 1-41. | Zbl

[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. | Zbl

[12] J. Rutten, Universal coalgebra, a theory of systems. Theoret. Comput. Sci. 249 (2000) 3-80. | Zbl

[13] P. Taylor, Practical Foundations of Mathematics. Cambridge University Press (1999). | MR | Zbl

[14] V. Trnková, On a descriptive classification of set-functors I. Comment. Math. Univ. Carolin. 12 (1971) 143-174. | EuDML | Zbl

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