nLab
braided infinity-group

Context

Group Theory

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

Contents

Definition

Definition

An ∞-group GG is braided if it is equipped with the following equivalent structure

  1. Regarded as a monoidal (∞,1)-category, GG is a braided monoidal (∞,1)-category.

  2. The delooping ∞-groupoid BG\mathbf{B}G has the structure of an ∞-group.

  3. The double delooping ∞-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 (∞,0)-category.

Examples

See the examples at braided 2-group, braided 3-group.

Revised on December 12, 2012 16:49:59 by Urs Schreiber (71.195.68.239)