\begin{definition}[Definition:Set Product/Projection]
Let $\family {S_i}_{i \mathop \in I}$ be an indexed family of sets.
Let $\struct {P, \family {\phi_i}_{i \mathop \in I} }$ be a set product of $\family {S_i}_{i \mathop \in I}$.
The mappings $\phi_i$ are the '''projections''' of $P$.
\end{definition}