Cardinality in allegories

Authors:
Yasuo Kawahara;Michael Winter
Affiliations:
Department of Informatics, Kyushu University, Fukuoka, Japan;Department of Computer Science, Brock University, St. Catharines, Ontario, Canada
Venue:
RelMiCS'08/AKA'08 Proceedings of the 10th international conference on Relational and kleene algebra methods in computer science, and 5th international conference on Applications of kleene algebra
Year:
2008

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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.