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braided 2-group

Contents

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

Under the name “braided gr-categories” or “braided cat-groups” and thought of as a sub-class of braided monoidal categories, the notion of braided 2-groups is considered in:

As a special case of k-tuply groupal n-groupoids:

In the generality of braided ∞-group stacks the notion appears in

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

Last revised on July 21, 2021 at 11:31:15. See the history of this page for a list of all contributions to it.