Grothendieck ring

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 $\Lambda$-ring — even better.

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

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