nLab sylleptic ∞-group

Definition

A sylleptic $\infty$-group is an ∞-group $G$ equipped with the following equivalent structure

1. a lift of its A-∞/E1-algebra structure to an E3 algebra structure;

2. the structure of a braided ∞-group on its delooping $\mathbf{B}G$

3. the structure of an ∞-group on its double delooping $\mathbf{B}^2 G$

4. a triple delooping $\mathbf{B}^3 G$.

Related concepts

• sylleptic monoidal 2-category

• ∞-group, k-tuply groupal n-groupoid

• May recognition theorem

• braided ∞-group,

  • braided 2-group

  • braided 3-group

• sylleptic ∞-group

  • sylleptic 3-group

• abelian ∞-group

  • symmetric 2-group

References

On sylleptic 3-groups:

• Nick Gurski, Angélica M. Osorno, Section 2.2 of Infinite loop spaces, and coherence for symmetric monoidal bicategories, Adv. Math. 246 (2013) 1-32 (arXiv:1210.1174)