nLab
(n,1)-category

Context

(,1)(\infty,1)-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

Contents

Idea

The special case of an (n,r)-category for r=1r = 1.

Definition

An (n,1)(n,1)-category, is an nn-category CC that is locally (n1)(n-1)-groupoidal; that is, for any objects xx and yy, the (n1)(n-1)-category C(x,y)C(x,y) is an (n1)(n-1)-groupoid.

Special cases:

Extra stuff, structure, property

  • An (n,1)(n,1)-category with the abalogous properties of a topos is an (n,1)-topos.

Examples

The canonical example of an (n+1,1)(n+1,1)-category is nGrpd.

Revised on April 27, 2011 20:27:20 by Urs Schreiber (131.211.239.98)