• The Colimit. The set $\coprod _{i\in I}A_{i}$ defined by
    \[ \coprod _{i\in I}A_{i}\mathrel {\smash {\overset {\mathclap {\scriptscriptstyle \text{def}}}=}}\webleft\{ \webleft (i,x\webright )\in I\times \webleft(\bigcup _{i\in I}A_{i}\webright)\ \middle |\ \text{$x\in A_{i}$}\webright\} . \]

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