Isomorphic objects in symmetric monoidal closed categories

Mathematical Structures in Computer Science - Tập 7 Số 6 - Trang 639-662 - 1997
Kosta Došen1, Zoran Petrić2
1University 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, 1100 ...#TAB#
2University of Belgrade, Faculty of Mining and Geology, Djušina 7, 11000 Belgrade, Yugoslavia#TAB#

Tóm tắt

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.

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Mathematical Structures in Computer Science

Tập 7 Số 6

639-662

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