amalg
Represents the disjoint union or amalgamation operation in mathematical set theory and algebra.
Overview
Commonly used in advanced mathematics to denote the union of sets that are explicitly kept distinct or separate, even when their elements might otherwise be identical.
- Essential in category theory for describing coproducts and direct sums
- Appears frequently in algebraic topology when combining topological spaces
- Used in set theory to indicate that sets should remain distinguishable in their union
- Particularly useful in abstract algebra when working with group theory and ring theory
Examples
Disjoint union of sets A and B.
A \amalg B = \{(x,1) : x \in A\} \cup \{(x,2) : x \in B\}Representing the coproduct of algebraic structures.
G \amalg H \cong K