nLab symmetric 3-group

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.

Related concepts

• k-tuply groupal n-groupoid