The Colimit. The set $A\mathchoice {\mathbin {\textstyle \coprod }}{\mathbin {\textstyle \coprod }}{\mathbin {\scriptstyle \textstyle \coprod }}{\mathbin {\scriptscriptstyle \textstyle \coprod }}B$ defined by
\begin{align*} A\mathchoice {\mathbin {\textstyle \coprod }}{\mathbin {\textstyle \coprod }}{\mathbin {\scriptstyle \textstyle \coprod }}{\mathbin {\scriptscriptstyle \textstyle \coprod }}B & \mathrel {\smash {\overset {\mathclap {\scriptscriptstyle \text{def}}}=}}\coprod _{z\in \webleft\{ A,B\webright\} }z\\ & \mathrel {\smash {\overset {\mathclap {\scriptscriptstyle \text{def}}}=}}\webleft\{ \webleft (0,a\webright )\in S\ \middle |\ a\in A\webright\} \cup \webleft\{ \webleft (1,b\webright )\in S\ \middle |\ b\in B\webright\} , \end{align*}
where $S=\webleft\{ 0,1\webright\} \times \webleft (A\cup B\webright )$.