\begin{definition}[Definition:Bijective Restriction]
Let $f: S \to T$ be a mapping which is not bijective.
A '''bijective restriction''' of $f$ is a restriction $f {\restriction_{S' \times T'} }: S' \to T'$ of $f$ such that $f {\restriction_{S' \times T'} }$ is a bijection.
\end{definition}