Let $\mathscr{A}$ be a category, $I$ a set, and $(X_i){i \in I}$ a family of objects of $\mathscr{A}$. A product of $(X_i){i \in I}$ consists of an object $P$ and a family of maps \(\Bigl(P \stackrel{p_i}{\longrightarrow} X_i\Bigr)_{i \in I}\) with the property that for all objects $A$ and families of maps \(\Bigl(A \stackrel{f_i}{\longrightarrow} X_i\Bigr)_{i \in I}\) there exists a unique map $\bar{f}{\colon}\linebreak[0] A \to P$ such that $p_i \circ \bar{f} = f_i$ for all $i \in I$.