# nLab sylleptic 3-group

Contents

group theory

### Cohomology and Extensions

#### $(\infty,1)$-Category theory

(∞,1)-category theory

# Contents

## Definition

###### Definition

A sylleptic 3-group is a 3-group equipped with the following equivalent structure:

1. Regarded as a monoidal 2-category, $G$ is a sylleptic monoidal 2-category.

2. The A-∞ algebra/E1-algebra structure on $G$ refines to an E3-algebra structure.

3. $G$ is a 3-tuply monoidal 2-groupoid.

4. $G$ is a groupal 3-tuply monoidal (2,0)-category.

## Examples

Last revised on March 4, 2016 at 19:14:52. See the history of this page for a list of all contributions to it.