# nLab hom-groupoid

### Context

#### Enriched category theory

enriched category theory

## Extra stuff, structure, property

### Homotopical enrichment

#### Higher category theory

higher category theory

# Contents

## Idea

A $V$-enriched category $C$, for $V =$ Grpd (the category of groupoids), has for every ordered pair $x,y$ of objects a groupoid $C(x,y)$ of morphisms between $x$ and $y$. 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)