CRing - Category of Commutative Rings
Table of Contents
1. Definition
The category CRing consisting of:
- Objects
- Commutative, associative rings with identity
- Morphisms
- Ring morphisms
We can also consider the category of Monoid Objects in Ab the category of Abelian groups.
2. Properties
2.1. Cocartesian Co-Monoidal Structure
The coproduct in CRing is given by the underlying tensor product of Abelian groups equipped with the induced commutative ring structure.
The tensor product of commutative rings exhibits the cartesian monoidal category structure on the opposite category \(\cat{CRing}^{op}\).