# nLab topological groupoid

category theory

## Applications

#### Topology

topology

algebraic topology

# Contents

## Definition

### General

A topological groupoid is an internal groupoid in the category Top.

So this is a groupoid with a topological space of objects and one of morphisms, and all structure maps (source, target, identity, composition) are continuous maps.

A topological groupoid $C$ is called an open topological groupoid is the source map $s:\mathrm{Mor}C\to \mathrm{Obj}C$ is an open map.

It is called an étale groupoid if in addition $s$ is a local homeomorphism.

Created on October 18, 2010 16:54:03 by Urs Schreiber (131.211.232.170)