nLab braided infinity-group

Contents

Definition

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

Regarded as a monoidal (∞,1)-category, $G$ is a braided monoidal (∞,1)-category.
The delooping ∞-groupoid $\mathbf{B}G$ has the structure of an ∞-group.
The double delooping ∞-groupoid $\mathbf{B}^2 G$ exists.
The groupal A-∞ algebra/E1-algebra structure on $G$ refines to an E2-algebra structure.
$G$ is a doubly groupal ∞-groupoid.
$G$ is a groupal doubly monoidal (∞,0)-category.

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.