Coherence of Proof-Net Categories

Details Coherence of Proof-Net Categories Coherence of Proof-Net Categories

2005-03-15

arxiv.org/abs/math/0503301v3

Mathematics

Category Theory

40 pages, 1 figure

Scientific paper

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.

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