  The elliptic associator of Enriquez can be used to define an invariant of
tangles embedded in the thickened torus, which extends the Kontsevich integral.
This construction by Humbert uses the formulation of categories with elliptic
structures. In this work we show that an extension of the LMO functor also
leads to an elliptic structure on the category of Jacobi diagrams which is used
by the Kontsevich integral, and find the relation between the two structures.
We use this relation to give an alternative proof for the properties of the
elliptic associator of Enriquez. Those results can lead the way to finding
associators for higher genra.
