nLab
symmetric monoidal 2-category

Definition

A symmetric monoidal 2-category is a monoidal 2-category whose E1-algebra structure is refined to an E3-algebra structure.

A symmetric monoidal (infinity,n)-category for $n=2$.

Examples

• A symmetric monoidal 2-category all whose objects are invertible under the tensor product is a symmetric 3-group.

Related concepts

• monoidal 2-category, 3-group

• braided monoidal 2-category, braided 3-group

• sylleptic monoidal 2-category, sylleptic 3-group

• symmetric monoidal 2-category, symmetric 3-group

• k-tuply monoidal (n,r)-category

References

• Mike Shulman, Constructing symmetric monoidal bicategories (arXiv:1004.0993v1)