note to @John – the second diagram in the lecture is wrong, it should look like this:

\[
\begin{matrix}
& & h & & \\\\
& c & \rightarrow & c' &\\\\
f & \uparrow & & \downarrow & g\\\\
& d & \rightarrow & d' &\\\\
& & ? & & \\\\
\end{matrix}
\]