  This paper explores several extensions of proof nets for the Lambek calculus
in order to handle the different connectives of display logic in a natural way.
The new proof net calculus handles some recent additions to the Lambek
vocabulary such as Galois connections and Grishin interactions. It concludes
with an exploration of the generative capacity of the Lambek-Grishin calculus,
presenting an embedding of lexicalized tree adjoining grammars into the
Lambek-Grishin calculus.
