A binary operator representing the disjoint union of sets or the union of disjoint collections in set theory.
Examples
Disjoint union of sets
A \doublecup B \text{ represents the disjoint union of sets A and B}
Multiple disjoint union
X = A_1 \doublecup A_2 \doublecup A_3
Disjoint union with index notation
\bigsqcup_{i=1}^n A_i = A_1 \doublecup A_2 \doublecup \cdots \doublecup A_n