# nLab fully dualizable object

### Context

#### Monoidal categories

monoidal categories

## In higher category theory

#### Higher category theory

higher category theory

duality

# Contents

## Idea

A dualizable object in a symmetric monoidal (∞,n)-category is called fully dualizable if the structure maps of the duality unit and counit each themselves have adjoints, which have adjoints, and so on.

## Properties

By the cobordism hypothesis-theorem, symmetric monoidal (∞,n)-functors out of the (∞,n)-category of cobordisms are characterized by their value on the point, which is a fully dualizable object.

finite objects:

## References

The definition appears around claim 2.3.19 of

Revised on September 4, 2014 08:28:18 by David Corfield (129.12.18.225)