Coherence of Proof-Net Categories
نویسندگان
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 1 v 2 [ m at h . C T ] 9 S ep 2 00 5 Coherence of Proof - Net Categories
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 ...
متن کاملNATURAL DEDUCTION AND COHERENCE FOR NON - SYMMETRIC LINEARLY DISTRIBUTIVE CATEGORIES Dedicated to Joachim Lambek
In this paper certain proof-theoretic techniques of [BCST] are applied to non-symmetric linearly distributive categories, corresponding to non-commutative negation-free multiplicative linear logic (mLL). First, the correctness criterion for the two-sided proof nets developed in [BCST] is adjusted to work in the non-commutative setting. Second, these proof nets are used to represent morphisms in...
متن کاملExtracting a Proof of Coherence for Monoidal Categories from a Proof of Normalization for Monoids
This paper studies the problem of coherence in category theory from a type-theoretic viewpoint. We rst show how a Curry-Howard interpretation of a formal proof of normalization for monoids almost directly yields a coherence proof for monoidal categories. Then we formalize this coherence proof in intensional intuitionistic type theory and show how it relies on explicit reasoning about proof obje...
متن کاملCoherence of the Double Negation in Linear Logic
Many formulations of proof nets and sequent calculi for Classical Linear Logic (CLL) [7, 8] take it for granted that a type A is identical to its double negation A⊥⊥. On the other hand, since Seely [13], it has been assumed that ∗-autonomous categories [1, 2] are the appropriate semantic models of (the multiplicative fragment of) CLL. However, in general, in a ∗-autonomous category an object A ...
متن کاملCoherence for Skew-Monoidal Categories
We motivate a variation (due to K. Szlachányi) of monoidal categories called skew-monoidal categories where the unital and associativity laws are not required to be isomorphisms, only natural transformations. Coherence has to be formulated differently than in the well-known monoidal case. In my (to my knowledge new) version it becomes a statement of uniqueness of normalizing rewrites. We presen...
متن کامل