nLab
braided monoidal 2-category

Context

Monoidal categories

2-Category theory

Contents

Idea

A braided monoidal 2-category is a 2-category CC equipped with a tensor product :C×CC\otimes : C \times C \to C 2-functor which satisfies the first in a hierarchy of conditions for being commutative up to equivalence: in the language of k-tuply monoidal n-categories a braided monoidal 2-category is a doubly monoidal 2-category.

As described there, this may be identified with a pointed 4-category with a single object and a single 1-morphism.

Properties

Coherence theorem

Picard 2-groupoid

The Picard 2-groupoid of a braided monoidal 2-category is a braided 3-group.

References

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Revised on April 8, 2013 22:28:06 by Urs Schreiber (82.113.99.18)