  We compute the $g=1, n=1$ B-model Gromov-Witten invariant of an elliptic
curve E directly from the derived category D(E). More precisely, we carry out
the computation of the categorical Gromov-Witten invariant defined by Costello
using as target a cyclic $A_\infty$ model of D(E) described by Polishchuk.
  This is the first non-trivial computation of a positive genus categorical
Gromov-Witten invariant, and the result agrees with the prediction of mirror
symmetry: it matches the classical (non-categorical) Gromov-Witten invariants
of a symplectic 2-torus computed by Dijkgraaf.
