nLab
symmetric monoidal 2-category

Context

Higher category theory

higher category theory

Basic concepts

Basic theorems

Applications

Models

Morphisms

Functors

Universal constructions

Extra properties and structure

1-categorical presentations

Higher algebra

Contents

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=2n = 2.

A (fully) strict symmetric monoidal 2-category is simply a strict 22-category 𝒞\mathcal{C} together with a strict 2-functor :𝒞×𝒞𝒞\otimes : \mathcal{C} \times \mathcal{C} \rightarrow \mathcal{C} and an object 11 of 𝒞\mathcal{C} which satisfy the same axioms as for a strict symmetric monoidal category (which in turn are exactly the same as those for a commutative monoid).

Examples

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

References

Revised on May 22, 2017 15:19:53 by Richard Williamson (84.202.247.109)