A large binary operator representing disjoint union of sets or indexed families in set theory and topology.
Examples
Disjoint union of sets
X = \bigsqcup_{i=1}^n A_i
Direct sum of vector spaces
V = \bigsqcup_{k=1}^m V_k \text{ where } V_k \text{ are subspaces}
Decomposition into disjoint subsets
\Omega = \bigsqcup_{j \in J} E_j \text{ where } E_i \cap E_j = \emptyset \text{ for } i \neq j