Definition 5.71.
For \(u\colon A \to B\) and \(v\colon C \to D\), the pushout product
\[u \ssquare v\colon (B \times C) \sqcup_{A \times C} (A \times D) \longrightarrow B \times D\]
is the cogap map of the commutative square
We already encountered this operation before in Notation 5.15.