# nLab sylleptic ∞-group

Contents

group theory

### Cohomology and Extensions

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

(∞,1)-category theory

# Contents

## Definition

A sylleptic $\infty$-group is an ∞-group $G$ equipped with the following equivalent structure

1. a lift of its A-∞/E1-algebra structure to an E3 algebra structure;

2. the structure of a braided ∞-group on its delooping $\mathbf{B}G$

3. the structure of an ∞-group on its double delooping $\mathbf{B}^2 G$

4. a triple delooping $\mathbf{B}^3 G$.

Created on November 30, 2012 at 22:16:15. See the history of this page for a list of all contributions to it.