Proof nets, coends and the Yoneda isomorphism

## Author: Paolo Pistone

## Paper Information

Title: | Proof nets, coends and the Yoneda isomorphism |

Authors: | Paolo Pistone |

Proceedings: | Linearity/TLLA Pre-proceedings |

Editors: | Maribel Fernandez, Valeria de Paiva, Thomas Ehrhard and Lorenzo Tortora De Falco |

Keywords: | Proof nets, second order quantifiers, multiplicative linear logic, coends, Yoneda isomorphism |

Abstract: | ABSTRACT. Proof nets provide permutation-independent 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. By adapting the "rewiring approach" used in the proof net characterization of the free *-autonomous category, we provide a compact representation of proof nets for a fragment of MLL2 related to the Yoneda isomorphism. We prove that the equivalence generated by coends over proofs in this fragment is fully characterized by the rewiring equivalence over proof nets. |

Pages: | 12 |

Talk: | Jul 07 17:00 (Session 31J) |

Paper: |