We consider the classification problem for rank 4 premodular categories. We uncover a formula for the 2^nd Frobenius-Schur indicator of a premodular category, and complete the classification of rank 4 premodular categories (up to Grothendieck equivalence). In the appendix we show rank finiteness for premodular categories.

PNNL Information Release: PNNL-SA-111549. A portion of this paper was produced at a workshop at the American Institute of Mathematics, whose support and hospitality are gratefully acknowledged. The research described in this paper was, in part, conducted under the Laboratory Directed Research and Development Program at PNNL, a multi-program national laboratory operated by Battelle for the U.S. Department of Energy.