nLab symmetric 3-group

group theory

Cohomology and Extensions

$(\infty,1)$-Category theory

(∞,1)-category theory

Contents

Definition

A symmetric 3-group is the following equivalent structure

1. A 3-group whose E1-algebra structure is equipped with a lift to to an E4-algebra structure.

2. A 3-group which regarded as an ∞-group is equipped with the structure of an abelian ∞-group.

3. A 3-group such that the delooping $\mathbf{B}G$ is equipped with the structure of a braided 4-group?.

4. A symmetric monoidal 2-category all whose objects are invertible under the tensor product.

Revised on November 1, 2012 18:15:30 by Urs Schreiber (131.174.41.102)