\doublecupThe \doublecup operator is used to denote the coproduct or disjoint union in category theory and algebra. It is similar to the union operator but emphasizes the distinctness of the elements being combined.
Coproduct of sets A and B
A \doublecup BCoproduct of multiple sets X, Y, and Z
X \doublecup Y \doublecup ZCoproduct of a family of sets A_i indexed by i
\bigdoublecup_{i=1}^{n} A_i