The coproduct of $\webleft\{ A_{i}\webright\} _{i\in I}$1 is the coproduct of $\webleft\{ A_{i}\webright\} _{i\in I}$ in $\mathsf{Sets}$ as in , .
1Further Terminology: Also called the disjoint union of the family $\webleft\{ A_{i}\webright\} _{i\in I}$.