Any abelian category C gives rise to an abelian group K(C) called its Grothendieck group. If we apply this construction to a monoidal abelian category, K(C) is a ring, called the Grothendieck ring.
If C is a braided monoidal category, K(C) becomes a commutative ring.
If C is a symmetric monoidal category, K(C) becomes a Λ-ring — even better.
If C is just braided monoidal, is K(C) just a commutative ring?