# nLab ring object

### Context

#### Algebra

higher algebra

universal algebra

category theory

# Contents

## Idea

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

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

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)