nLab
Grothendieck ring

Any abelian category CC gives rise to an abelian group K(C)K(C) called its Grothendieck group. If we apply this construction to a monoidal abelian category, K(C)K(C) is a ring, called the Grothendieck ring.

If CC is a braided monoidal category, K(C)K(C) becomes a commutative ring.

If CC is a symmetric monoidal category, K(C)K(C) becomes a Λ\Lambda-ring — even better.

If CC is just braided monoidal, is K(C)K(C) just a commutative ring?

Revised on July 30, 2009 18:56:12 by Toby Bartels (71.104.230.172)