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Point Axioms in Dedekind Categories

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Relational and Algebraic Methods in Computer Science (RAMICS 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7560))

Abstract

A Dedekind category is a convenient algebraic framework to treat relations. Concepts of points and some axioms such as the point axiom, the axiom of totality, the axiom of subobject, the axiom of complement, and the relational axiom of choice are introduced in Dedekind categories to connect functional ideas to set-theoretical intuition. This paper summarises interrelations of these axioms.

This work was supported in part by Grants-in-Aid for Scientific Research (C) 22500016 from Japan Society for the Promotion of Science (JSPS).

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Author information

Authors and Affiliations

  1. Department of Mathematics and Computer Science, Kagoshima University, Kagoshima, Japan

    Hitoshi Furusawa

  2. Kyushu University, Fukuoka, Japan

    Yasuo Kawahara

Authors
  1. Hitoshi Furusawa
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  2. Yasuo Kawahara
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Editor information

Editors and Affiliations

  1. Department of Computing and Software, McMaster University, 1280 Main Street West, L8S 4K1, Hamilton, ON, Canada

    Wolfram Kahl

  2. Computer Laboratory, University of Cambridge, 15 JJ Thomson Avenue, CB3 0FD, Cambridge, UK

    Timothy G. Griffin

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Furusawa, H., Kawahara, Y. (2012). Point Axioms in Dedekind Categories. In: Kahl, W., Griffin, T.G. (eds) Relational and Algebraic Methods in Computer Science. RAMICS 2012. Lecture Notes in Computer Science, vol 7560. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33314-9_15

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  • DOI: https://doi.org/10.1007/978-3-642-33314-9_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-33313-2

  • Online ISBN: 978-3-642-33314-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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