# nLab braided monoidal (∞,1)-category

### Context

#### Monoidal categories

monoidal categories

## In higher category theory

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

(∞,1)-topos theory

## Constructions

structures in a cohesive (∞,1)-topos

#### Higher algebra

higher algebra

universal algebra

# Contents

## Definition

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

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

Created on October 26, 2012 03:53:34 by Urs Schreiber (82.169.65.155)