nLab
fully dualizable object

Contents

Context

Monoidal categories

monoidal categories

With symmetry

With duals for objects

With duals for morphisms

With traces

Closed structure

Special sorts of products

Semisimplicity

Morphisms

Internal monoids

Examples

Theorems

In higher category theory

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 𝒞\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 (n1)(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.

Examples

finite objects:

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