nLab
3-group

Context

Group Theory

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

Contents

Definition

A 3-group is equivalently

  1. a 2-truncated ∞-group;

  2. a 2-groupoid GG equipped with the structure of a loop space object of a connected 3-groupoid BG\mathbf{B}G (its delooping);

  3. a monoidal 2-category in which every object has an weak inverse under the tensor product.

Properties

Presentation by crossed complexes

Some classes of 3-groups are modeled by 2-crossed modules or crossed squares.

Revised on November 1, 2012 18:10:54 by Urs Schreiber (131.174.41.102)