The Clowder Project

\[ \prod _{i\in I}A_{i} \mathrel {\smash {\overset {\mathclap {\scriptscriptstyle \text{def}}}=}}\webleft\{ f\in \mathsf{Sets}\webleft(I,\bigcup _{i\in I}A_{i}\webright)\ \middle |\ \text{for each $i\in I$, we have $f\webleft (i\webright )\in A_{i}$}\webright\} . \]