nLab
Grothendieck ring

Any abelian category CC gives rise to an abelian group K(C)K(C) called its Grothendieck group (see there for more). If we apply this construction to a monoidal abelian category or generally to a rig 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?

Last revised on September 12, 2018 at 05:39:55. See the history of this page for a list of all contributions to it.