nLab
braided monoidal (∞,1)-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

(,1)(\infty,1)-topos theory

(∞,1)-topos theory

Background

Definitions

Characterization

Morphisms

Extra stuff, structure and property

Models

Constructions

structures in a cohesive (∞,1)-topos

Higher algebra

Contents

Definition

Where a monoidal (∞,1)-category is an E1-algebra in (∞,1)Cat, a braided monoidal (,1)(\infty,1)-category is an E2-algebra in (∞,1)Cat.

If the (∞,1)-category 𝒞\mathcal{C} underlying a braided monoidal (,1)(\infty,1)-category (𝒞,)(\mathcal{C}, \otimes) is a 1-category, then (𝒞,)(\mathcal{C}, \otimes) is a braided monoidal category.

Created on October 26, 2012 at 03:53:37. See the history of this page for a list of all contributions to it.