nLab
fully dualizable object

Context

Monoidal categories

Higher category theory

higher category theory

Basic concepts

Basic theorems

Applications

Models

Morphisms

Functors

Universal constructions

Extra properties and structure

1-categorical presentations

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.

Examples

finite objects:

geometrymonoidal category theorycategory theory
perfect module(fully-)dualizable objectcompact object

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)