# nLab union

### Context

#### Limits and colimits

limits and colimits

# Contents

## Definition

A union is a join of subsets or (more generally) subobjects. This includes the traditional set-theoretic union of subsets of some ambient set.

The dual notion is that of intersection/meet.

Unions of completely arbitrary sets make sense only in material set theory, where their existence is guaranteed by the axiom of union. In structural set theory, unions of arbitrary sets can generally be replaced by disjoint unions.

A coherent category is one having well-behaved unions of subobjects.

## Properties

Revised on May 20, 2017 13:21:21 by Urs Schreiber (92.218.150.85)