The _disjoint union_ of two [sets](Sets.md), $A,$ and $B,$ is the set, $A \amalg B$ such that [$A'\cap B'=\emptyset$](Intersection%20of%20sets.md) where $A'$ and $B'$ are are copies of $A$ and $B$ that are [disjoint.](Intersection%20of%20sets.md#Disjoint%20sets) # As a coproduct of the category of sets #MathematicalFoundations/SetTheory