nLab
(infinity,n)Cat

Context

Higher category theory

higher category theory

Basic concepts

Basic theorems

Applications

Models

Morphisms

Functors

Universal constructions

Extra properties and structure

1-categorical presentations

categories of categories

Contents

Idea

The (large) (,n+1)(\infty,n+1)-category (,n)Cat(\infty,n)Cat is the collection of all (small) (∞,n)-categories:

There are various presentations for this. For general nn see for instance this section at Theta-space. For low nn see the discussion at (∞,1)Cat and (∞,2)Cat?.

Often it is useful to consider just the maximal (∞,1)-category inside (,n)Cat(\infty,n)Cat. This is what is presented by various model category structures on models for (,n)(\infty,n)-categories.

The discussion in (BarwickSchommer-Pries) shows that essentially all proposed models for (,n)Cat(\infty,n)Cat are in fact equivalent.

Properties

Automorphisms

The automorphism ∞-group of (,n)Cat(\infty,n)Cat is equivalent to ( 2) n(\mathbb{Z}_2)^n.

This is due to (Barwick & Schommer-Pries).

(See also at duality.)

References

category: category

Revised on February 27, 2014 08:31:34 by Urs Schreiber (82.113.98.143)