nLab
sylleptic monoidal 2-category

Context

Monoidal categories

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.

Revised on October 10, 2017 17:05:46 by Mike Shulman (76.167.222.204)