# nLab tensor ring

Contents

### Context

#### Algebra

higher algebra

universal algebra

group theory

# Contents

## Idea

A free monoid object in Ab

## Definition

Given an abelian group $G$, the tensor ring is a ring $T(G)$ with an abelian group homomorphism $g:G \to T(G)$, such that for every other ring $R$ with abelian group homomorphism $h:G \to R$, there is a unique ring homomorphism $i:T(G) \to R$ such that $i \circ g = h$.