equivalences in/of $(\infty,1)$-categories
A symmetric 3-group is the following equivalent structure
A 3-group whose E1-algebra structure is equipped with a lift to to an E4-algebra structure.
A 3-group which regarded as an ∞-group is equipped with the structure of an abelian ∞-group.
A 3-group such that the delooping $\mathbf{B}G$ is equipped with the structure of a braided 4-group?.
A symmetric monoidal 2-category all whose objects are invertible under the tensor product.