Abstract
In this paper we want to investigate two notions of the cardinality of relations in the context of allegories. The different axiom systems are motivated on the existence of injective and surjective functions, respectively. In both cases we provide a canonical cardinality function and show that it is initial in the category of all cardinality functions over the given allegory.
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Berghammer, R.: Computation of Cut Completions and Concept Lattices Using Relational Algebra and RelView. JoRMiCS 1, 50–72 (2004)
Bird, R., de Moor, O.: Algebra of Programming. Prentice-Hall, Englewood Cliffs (1997)
Brink, C., Kahl, W., Schmidt, G. (eds.): Relational Methods in Computer Science. Advances in Computer ScienceVienna. Springer, Vienna (1997)
Freyd, P., Scedrov, A.: Categories, Allegories. North-Holland, Amsterdam (1990)
Grätzer, G.: General lattice theory, 2nd edn. Birkhäuser, Basel (2003)
Kawahara, Y.: On the Cardinality of Relations. In: Schmidt, R.A. (ed.) RelMiCS/AKA 2006. LNCS, vol. 4136, pp. 251–265. Springer, Heidelberg (2006)
Kawahara, Y., Winter, M.: On the Tabular Closure of a Sub-Allegory of a Tabular Allegory (to appear)
Schmidt, G., Ströhlein, T.: Relationen und Graphen. Springer, Heidelberg (1989); English version: Relations and Graphs. Discrete Mathematics for Computer Scientists, EATCS Monographs on Theoret. Comput. Sci., Springer, Heidelberg (1993).
Winter, M.: Goguen Categories. A Categorical Approach to L-Fuzzy Relations. Trends in Logic 25 (2007)
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Kawahara, Y., Winter, M. (2008). Cardinality in Allegories. In: Berghammer, R., Möller, B., Struth, G. (eds) Relations and Kleene Algebra in Computer Science. RelMiCS 2008. Lecture Notes in Computer Science, vol 4988. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78913-0_21
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DOI: https://doi.org/10.1007/978-3-540-78913-0_21
Publisher Name: Springer, Berlin, Heidelberg
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