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 $\mathcal{C}$ 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.

finite objects:

References

The definition appears around claim 2.3.19 of

Detailed discussion in degree 2 and 3 appears in

Revised on October 24, 2014 08:40:11 by Urs Schreiber (185.26.182.28)