# nLab symmetric ring groupoid

Contents

### Context

#### Algebra

higher algebra

universal algebra

categorification

category theory

# Contents

## Idea

A symmetric ring groupoid is a 1-truncated $E_\infty$-ring.

Equivalently: A groupoid $G$ that is both a symmetric 2-group $(G, 0, \oplus)$ and a symmetric monoidal groupoid $(G, 1, \otimes)$ such that $\otimes$ distributes over $\oplus$ satisfying certain higher coherence laws (given in Kelly74).

## Properties

• G. M. Kelly, Coherence theorems for lax algebras and distributive laws, Lecture Notes in Mathematics 420, Springer Verlag, Berlin(1974) 281-375 $[$doi:10.1007/BFb0063106$]$