nLab
union

Contents

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

Last revised on May 20, 2017 at 13:21:21. See the history of this page for a list of all contributions to it.