Authors: Došen, Kosta 
Petrić, Zoran 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Isomorphic objects in symmetric monoidal closed categoriest
Journal: Mathematical Structures in Computer Science
Volume: 7
Issue: 6
First page: 639
Last page: 662
Issue Date: 1-Jan-1997
Rank: M22
ISSN: 0960-1295
DOI: 10.1017/S0960129596002241
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 T = 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.
Publisher: Cambridge University Press

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