Authors: Došen, Kosta 
Petrić, Zoran 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Coherence of Proof-Net Categories
Journal: Publications de l'Institut Mathématique
Volume: 78
Issue: 92
First page: 1
Last page: 33
Issue Date: 2005
Rank: M24
ISSN: 0350-1302
URL: http://elib.mi.sanu.ac.rs/files/journals/publ/98/n092p001.pdf
Abstract: 
The notion of proof-net category defined in this paper is closely related to graphs implicit in proof nets for the multiplicative fragment without constant propositions of linear logic. Analogous graphs occur in Kelly’s and Mac Lane’s coherence theorem for symmetric monoidal closed categories. A coherence theorem with respect to these graphs is proved for proof-net categories. Such a coherence theorem is also proved in the presence of arrows corresponding to the mix principle of linear logic. The notion of proof-net category catches the unit free fragment of the notion of star-autonomous category, a special kind of symmetric monoidal closed category.
Publisher: Mathematical Institute of the SASA

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