# nLab sylleptic monoidal 2-category

Contents

### Context

#### Monoidal categories

monoidal categories

## In higher category theory

#### 2-Category theory

2-category theory

# Contents

## Idea

A sylleptic monoidal (weak) 2-category is a monoidal 2-category with a categorified sort of “commutativity” that lies in between a braiding and a symmetry.

That is, it is a 2-category $C$ equipped with a tensor product $\otimes : C \times C \to C$ 2-functor which satisfies the first two 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 triply monoidal 2-category. As described there, this may be identified with a pointed 5-category with a single $k$-morphism for $k=0,1,2$. We can also say that it is a monoidal 2-category whose E1-algebra structure is refined to an E3-algebra structure.

Last revised on October 10, 2017 at 17:05:46. See the history of this page for a list of all contributions to it.