nLab
braided 2-group

Definition

Definition

A 2-group $G$ is braided if it is equipped with the following equivalent structure:

1. Regarded as a monoidal category, $G$ is a braided monoidal category.

2. The delooping 2-groupoid $BG$ is a 3-group.

3. The double delooping 3-groupoid $B^{2}G$ exists.

4. The groupal A-∞ algebra/E1-algebra structure on $G$ refines to an E2-algebra structure.

5. $G$ is a doubly groupal groupoid.

6. $G$ is a groupal doubly monoidal (1,0)-category.

Related concepts

• k-tuply groupal n-groupoid

• symmetric 2-group

• braided ∞-group

References

A discussion of ∞-group extensions by braided 2-groups is in

• Evan Jenkins, Extensions of groups by braided 2-groups (arXiv:1106.0772)