Geodesic
Coherence of Proof-net Categories
Publications de l'Institut Mathématique, _N_S_78 (2005) no. 92, p. 1 .

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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.
Classification : 03F07 03F52 18D10 18D15 19D23
Keywords: generality of proofs, linear logic, mix, proof nets, linear distribution, dissociativity, categorial coherence, Kelly-Mac Lane graphs, Brauerian graphs, split equivalences, symmetric monoidal closed category, star-autonomous category 
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     author = {Kosta Do\v{s}en and Zoran Petri\'c},
     title = {Coherence of {Proof-net} {Categories}},
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     number = {92},
     year = {2005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PIM_2005_N_S_78_92_a0/}
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Kosta Došen; Zoran Petrić. Coherence of Proof-net Categories. Publications de l'Institut Mathématique, _N_S_78 (2005) no. 92, p. 1 . http://geodesic.mathdoc.fr/item/PIM_2005_N_S_78_92_a0/