# nLab fully dualizable object

Contents

### 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 $\mathcal{C}$ is called fully dualizable if the structure maps of the duality unit and counit each themselves have adjoints, which have adjoints, and so on, up to level $(n-1)$.

## 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.

## References

The definition appears around claim 2.3.19 of

Detailed discussion in degree 2 and 3 appears in

Last revised on April 29, 2016 at 12:47:14. See the history of this page for a list of all contributions to it.