nLab
hom-groupoid

Context

Enriched 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

A VV-enriched category CC, for V=V = Grpd (the category of groupoids), has for every ordered pair x,yx,y of objects a groupoid C(x,y)C(x,y) of morphisms between xx and yy. This hom-object is hence a hom-groupoid in this case.

For this reason such a category may be thought of as a locally groupoidal 2-category, or (2,1)-category.

Examples

Revised on September 14, 2010 16:48:49 by Toby Bartels (75.88.91.32)