nLab braided infinity-group

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Context

Group Theory

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

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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.

References

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

Last revised on July 21, 2021 at 15:08:58. See the history of this page for a list of all contributions to it.