👉 In mathematics and physics, a coproduct is an operation on a set of elements. It is often used in the context of algebraic structures such as groups, rings, and algebras. A coproduct is defined by associativity: given two coproducts $\Delta$ and $E$, we have: $$\Delta E = \sum_{x} (\Delta x) E$$ where $x \in X$ is an element of the set $X$