Abstract
We investigate how finitary functors on Set can be extended or lifted to finitary functors on Preord and Poset and discuss applications to coalgebra.
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Abramsky, S., Jung, A.: Domain Theory. In: Abramsky, S., Gabbay, D.M., Maibaum, T.S.E. (eds.) Handbook of Logic in Computer Science, vol. 3, pp. 1–168. Oxford Univ. Press, New York (1994)
Aczel, P., Mendler, N.: A Final Coalgebra Theorem. In: Dybjer, P., Pitts, A.M., Pitt, D.H., Poigné, A., Rydeheard, D.E. (eds.) Category Theory and Computer Science. LNCS, vol. 389, pp. 357–365. Springer, Heidelberg (1989)
Adámek, J.: Final Coalgebras Are Ideal Completions of Initial Algebras. J. Logic Computat. 12(2), 217–242 (2002)
Adámek, J., Trnková, V.: Automata and Algebras in Categories. Mathematics and Its Applications: East European Series, vol. 37. Kluwer Academic Publishers, Dordrecht (1990)
Bilková, M., Kurz, A., Petrişan, D., Velebil, J.: Relation Liftings on Preorders and Posets. In: Corradini, A., Klin, B., Crstea, C. (eds.) CALCO 2011. LNCS, vol. 6859, pp. 115–129. Springer, Heidelberg (2011)
Borceux, F.: Handbook of Categorical Algebra. In: Encycl. Mathem. Appl., vol. 50-52. Cambridge Univ. Press, Cambridge (1994)
Guitart, R.: Relations et Carrés Exacts. Ann. Sci. Math. Québec 4(2), 103–125 (1980)
Hughes, J., Jacobs, B.: Simulations in Coalgebra. Theor. Comput. Sci. 327, 71–108 (2004)
Kapulkin, K., Kurz, A., Velebil, J.: Expressivity of Coalgebraic Logic over Posets. In: Jacobs, B.P.F., Niqui, M., Rutten, J.J.M.M., Silva, A.M. (eds.) CMCS 2010 Short contributions, CWI Technical report SEN-1004, pp. 16–17 (2010)
Karazeris, P., Matzaris, A., Velebil, J.: Final Coalgebra in Accessible Categories, http://xxx.lanl.gov/abs/0905.4883
Lambek, J.: Subequalizers. Canad. Math. Bull. 13, 337–349 (1970)
Levy, P.: Similarity Quotients as Final Coalgebras. In: Hofmann, M. (ed.) FOSSACS 2011. LNCS, vol. 6604, pp. 27–41. Springer, Heidelberg (2011)
Rutten, J.: Relators and Metric Bisimulations (Extended Abstract). In: Jacobs, B., Moss, L., Reichel, H., Rutten, J. (eds.) First Workshop on Coalgebraic Methods in Computer Science, CMCS 1998. Electr. Notes Theor. Comput. Sci., vol. 11, pp. 252–258 (1998)
Rutten, J.: Universal Coalgebra: A Theory of Systems. Theor. Comput. Sci. 249, 3–80 (2000)
Thijs, A.: Simulation and Fixed Point Sematics, Ph. D. Thesis, University of Groningen (1996)
Velebil, J., Kurz, A.: Equational Presentations of Functors and Monads. Math. Struct. Comput. Sci. 21(2), 363–381 (2011)
Worrell, J.: Coinduction for Recursive Data Types: Partial orders, Metric Spaces and Ω-Categories. In: Reichel, H. (ed.) Coalgebraic Methods in Computer Science, CMCS 2000. Electr. Notes Theor. Comput. Sci., vol. 33, pp. 337–356 (2000)
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Balan, A., Kurz, A. (2011). Finitary Functors: From Set to Preord and Poset . In: Corradini, A., Klin, B., Cîrstea, C. (eds) Algebra and Coalgebra in Computer Science. CALCO 2011. Lecture Notes in Computer Science, vol 6859. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22944-2_7
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DOI: https://doi.org/10.1007/978-3-642-22944-2_7
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