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A binary operator representing disjoint unions or coproducts, commonly used in category theory and set theory.

\amalg image

Examples

Disjoint union of sets

A \amalg B \amalg C = \{(x,1):x\in A\} \cup \{(x,2):x\in B\} \cup \{(x,3):x\in C\}

Coproduct in category theory

X = X_1 \amalg X_2 \amalg X_3

Disjoint union of topological spaces

\text{Top}(X, Y_1 \amalg Y_2) \cong \text{Top}(X,Y_1) \times \text{Top}(X,Y_2)