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, and unions of arbitrary subsets are represented by wide pushouts of the corresponding injections from the intersection of the subsets.
A coherent category is one having well-behaved finite unions of subobjects, and an infinitary coherent category is one having all well-behaved small unions of subobjects.
Last revised on May 25, 2023 at 16:10:33. See the history of this page for a list of all contributions to it.