# 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, inverse) are continuous maps.

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

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

## Properties

### Relation to toposes

Every topos (Grothendieck topos) with enough points is the classifying topos of a topological groupoid. See there for more.

Revised on June 3, 2017 05:16:05 by Urs Schreiber (178.6.236.87)