Finite matrices are complete for (dagger-)hypergraph categories

Abstract: Hypergraph categories are symmetric monoidal categories where each object is equipped with a special commutative Frobenius algebra (SCFA). Dagger-hypergraph categories are the same, but with dagger-symmetric monoidal categories and dagger-SCFAs. In this paper, we show that finite matrices over a field K of characteristic 0 are complete for hypergraph categories, and that finite matrices where K has a non-trivial involution are complete for dagger-hypergraph categories.