# nLab invertible object

Contents

### Context

#### Monoidal categories

monoidal categories

duality

# Contents

## Definition

###### Definition

In a monoidal category, a dualizable object $A$ for which the structure unit (and counit) maps between $A \otimes A^\ast$ (and $A^\ast \otimes A$) and the unit object are isomorphisms is called an invertible object.

###### Remark

A monoidal category in which all objects are invertible is called a 2-group.

###### Definition

In terms of linear type theory one might speak of invertible types.

Last revised on May 22, 2017 at 14:37:30. See the history of this page for a list of all contributions to it.