EMIS ELibM Electronic Journals Publications de l'Institut Mathématique, Nouvelle Série
Vol. 82(96), pp. 17–23 (2007)

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Kosta Dosen and Zoran Petric

Mathematicki Institut SANU, Knez Mihailova 35, 11001 Beograd p.p. 367, Serbia

Abstract: A relevant category is a symmetric monoidal closed category with a diagonal natural transformation that satisfies some coherence conditions. Every cartesian closed category is a relevant category in this sense. The denomination \emph{relevant} comes from the connection with relevant logic. It is shown that the category of sets with partial functions, which is isomorphic to the category of pointed sets, is a category that is relevant, but not cartesian closed.

Keywords: symmetric monoidal closed categories; diagonal natural transformation; intuitionistic relevant logic; partial functions; pointed sets

Classification (MSC2000): 03B47; 03F52, 03G30, 18D10, 18D15

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Electronic fulltext finalized on: 20 Feb 2008. This page was last modified: 26 Feb 2008.

© 2008 Mathematical Institute of the Serbian Academy of Science and Arts
© 2008 ELibM and FIZ Karlsruhe / Zentralblatt MATH for the EMIS Electronic Edition