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Isomorphic objects in symmetric monoidal closed categories

Published online by Cambridge University Press:  01 December 1997

KOSTA DOšEN  and
ZORAN PETRIĆ
KOSTA DOšEN
Affiliation:
University of Toulouse III, Institut de Recherche en Informatique de Toulouse, 118 route de Narbonne, 31062 Toulouse cedex, France and Mathematical Institute, Knez Mihailova 35, P.O. Box 367, 11001 Belgrade, Yugoslavia
ZORAN PETRIĆ
Affiliation:
University of Belgrade, Faculty of Mining and Geology, Djušina 7, 11000 Belgrade, Yugoslavia
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Abstract

This paper presents a new and self-contained proof of a result characterizing objects isomorphic in the free symmetric monoidal closed category, i.e., objects isomorphic in every symmetric monoidal closed category. This characterization is given by a finitely axiomatizable and decidable equational calculus, which differs from the calculus that axiomatizes all arithmetical equalities in the language with 1, product and exponentiation by lacking 1c=1 and (a · b)c=ac · bc (the latter calculus characterizes objects isomorphic in the free cartesian closed category). Nevertheless, this calculus is complete for a certain arithmetical interpretation, and its arithmetical completeness plays an essential role in the proof given here of its completeness with respect to symmetric monoidal closed isomorphisms.

Type
Research Article
Information
Mathematical Structures in Computer Science , Volume 7 , Issue 6 , December 1997 , pp. 639 - 662
Copyright
1997 Cambridge University Press

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Footnotes

Work on this paper was supported by Grant 0401A of the Science Fund of Serbia.