nLab
braided 2-group

Context

Group Theory

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

Contents

Definition

Definition

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

  1. Regarded as a monoidal category, GG is a braided monoidal category.

  2. The delooping 2-groupoid BG\mathbf{B}G is a 3-group.

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

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

  5. GG is a doubly groupal groupoid.

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

References

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

Revised on October 26, 2012 04:14:36 by Urs Schreiber (82.169.65.155)