nLab
CRing

The category CRingCRing

Definition

CRingCRing is the category of commutative rings and ring homomorphisms.

A commutative ring is a commutative monoid object in Ab, so CRing=CMon(Ab)CRing = CMon(Ab). As for commutative monoid objects in any symmetric monoidal category, the tensor product of commutative rings is again a commutative ring, and is the coproduct in CRingCRing; thus CRingCRing is cocartesian monoidal.

The opposite category CRing opCRing^{op} is the category of affine schemes.

Generalizations

category: category

Revised on August 27, 2011 07:48:04 by Urs Schreiber (89.204.153.103)