#
nLab

ribbon category

### 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

## Examples

## Theorems

## In higher category theory

## Definition

A **ribbon category** (also called a **tortile category**) is a braided pivotal category, or equivalently a balanced autonomous category, which satisfies $\theta^* = \theta$, where $\theta$ is the twist. This is a kind of category with duals.