Proof Nets, Coends and the Yoneda Isomorphism
Abstract
Proof nets provide permutationindependent representations of proofs and are used to investigate coherence problems for monoidal categories. We investigate a coherence problem concerning Second Order Multiplicative Linear Logic (MLL2), that is, the one of characterizing the equivalence over proofs generated by the interpretation of quantifiers by means of ends and coends. We provide a compact representation of proof nets for a fragment of MLL2 related to the Yoneda isomorphism. By adapting the "rewiring approach" used in coherence results for starautonomous categories, we define an equivalence relation over proof nets called "rewitnessing". We prove that this relation characterizes, in this fragment, the equivalence generated by coends.
 Publication:

arXiv eprints
 Pub Date:
 October 2018
 DOI:
 10.48550/arXiv.1810.01252
 arXiv:
 arXiv:1810.01252
 Bibcode:
 2018arXiv181001252P
 Keywords:

 Computer Science  Logic in Computer Science;
 Mathematics  Logic
 EPrint:
 In Proceedings LinearityTLLA 2018, arXiv:1904.06159