nLab
sylleptic monoidal 2-category

Contents

Context

Monoidal categories

monoidal categories

With symmetry

With duals for objects

With duals for morphisms

With traces

Closed structure

Special sorts of products

Semisimplicity

Morphisms

Internal monoids

Examples

Theorems

In higher 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 CC equipped with a tensor product :C×CC\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 kk-morphism for k=0,1,2k=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.