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symmetric 3-group

Context

Group Theory

(,1)(\infty,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 BG\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)