Editing Disjoint union (section)

== Category theory point of view ==

In [[category theory]] the disjoint union is defined as a [[coproduct]] in the category of sets. 

As such, the disjoint union is defined up to an isomorphism, and the above definition is just one realization of the coproduct, among others. When the sets are pairwise disjoint, the usual union is another realization of the coproduct. This justifies the second definition in the lead.

This categorical aspect of the disjoint union explains why <math>\coprod</math> is frequently used, instead of <math>\bigsqcup,</math> to denote ''coproduct''.