We know that every symmetric fusion category (SFC) gives rise to data
$N^{ij}_k$ that describe the fusion of simple objects:
$i\times j = N^{ij}_k k$, and the data $\theta_i =\pm 1$ that describe the twist of simple objects.

My question is what are the conditions on the data $N^{ij}_k,\theta_i$ such that the data correspond to a SFC?

Any condition is welcome.