nLab
ring object

Context

Algebra

Category theory

Contents

Idea

For CC a cartesian monoidal category (a category with finite products), an internal ring or a ring object in CC is an internalization to the category CC of the notion of a ring.

This is a monoid object internal to the category of abelian group objects internal to CC.

Ring objects can be defined in more general symmetric monoidal categories as the corresponding module over a ring operad.

Examples

Revised on September 28, 2012 12:56:08 by Urs Schreiber (82.169.65.155)