  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.
  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 star-autonomous categories, we define an equivalence
relation over proof nets called "re-witnessing". We prove that this relation
characterizes, in this fragment, the equivalence generated by coends.
