theorem quasiTensorFunctor_induces_fusionRingHom {ι : Type} [DecidableEq ι] [Fintype ι] [Nonempty ι] {κ : Type} [DecidableEq κ] [Fintype κ] [Nonempty κ] (R : FusionRing ι) (S : FusionRing κ) : ∃ (φ : R.FusionRingHom S), ∀ (i : ι) (l : κ), 0 ≤ φ.M i l

A quasi-tensor functor between fusion rings induces a fusion ring homomorphism whose matrix entries are nonnegative, reflecting the categorical positivity of multiplicities under quasi-tensor functors.