Definition. Product of functions [dt-0026]

Given f : A \rightarrow C and g : B \rightarrow D, we overload the \times operator for products to denote the combined function f \times g : A \times B \rightarrow C \times D, given below:

\begin {array}{l} f \times g : A \times B \rightarrow C \times D \\ f \times g = \langle f \circ \pi _0 , g \circ \pi _1 \rangle \end {array}