What do we call the function in this diagram?

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We call the function f' in this diagrams:

[tex]\begin{displaymath}
\begin{xy}
*!C\xybox{
\xymatrix{
{E}\ar[r]^{i} \ar[d]_{f} & {X} \ar[dl]^{f'}\\
{Y} &}}
\end{xy}
\end{displaymath}
[/tex]
the entension of function f;
(i is an inclusion map)

[tex]\begin{displaymath}
\begin{xy}
*!C\xybox{
\xymatrix{
{E}\ar[r]^{i} \ar[dr]_{f'} & {X} \ar[d]^{f}\\
&{Y} }}
\end{xy}
\end{displaymath}
[/tex]
the restriction of function f;
(i is an inclusion map)

[tex]\begin{displaymath}
\begin{xy}
*!C\xybox{
\xymatrix{
&{E}\ar[d]^{p}\\
{X}\ar[ur]^{f'}\ar[r]_{f} & {Y} } }
\end{xy}
\end{displaymath}
[/tex]
the lifting of function f;

then how do we call the function f' in this this diagram:
[tex]\begin{displaymath}
\begin{xy}
*!C\xybox{
\xymatrix{
{X}\ar[r]^{f}\ar[rd]_{f'} & {Y} \ar[d]^{p}\\
&{E} } }
\end{xy}
\end{displaymath}
[/tex]
 
Oh,the latex codes do not display properly here.
So my question is what is the inverse of lifting? like restriction is the inverse of extension.
 

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