nLab (infinity,n)-category with duals

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Contents

Context

Higher category theory

higher category theory

Basic concepts

Basic theorems

Applications

Models

Morphisms

Functors

Universal constructions

Extra properties and structure

1-categorical presentations

Monoidal categories

monoidal categories

With braiding

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

Contents

Idea

An (∞,n)-category with adjoints (see there for more) and a (fully) dual object for every object.

Definition

Definition

Let CC be an (∞,n)-category. We say that

If CC is in addition a symmetric monoidal (∞,n)-category we say that

Finally we say that

  • CC has duals if it has duals for objects and has adjoints.

This is (Lurie, def. 2.3.13, def. 2.3.16). See at fully dualizable object

Properties

Internal language

The internal language of (,n)(\infty,n)-categories with duals seems plausible to be axiomatized inside opetopic type theory.

Examples

References

For more see at (infinity,n)-category with adjoints.

Last revised on November 17, 2022 at 12:40:57. See the history of this page for a list of all contributions to it.