ar X iv : m at h / 05 03 30 1 v 2 [ m at h . C T ] 9 S ep 2 00 5 Coherence of Proof - Net Categories
نویسنده
چکیده
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. Mathematics Subject Classification (2000): 03F07, 03F52, 18D10, 18D15, 19D23
منابع مشابه
ar X iv : m at h / 05 03 30 6 v 1 [ m at h . C T ] 1 5 M ar 2 00 5 Coherence for Star - Autonomous Categories
This paper presents a coherence theorem for star-autonomous categories exactly analogous to Kelly’s and Mac Lane’s coherence theorem for symmetric monoidal closed categories. The proof of this theorem is based on a categorial cut-elimination result, which is presented in some detail. Mathematics Subject Classification (2000): 03F05, 03F52, 18D10, 18D15, 19D23
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تاریخ انتشار 2005