What do we call the function in this diagram?

[navigator]

We call the function f' in this diagrams:

\begin{displaymath}<br /> \begin{xy}<br /> *!C\xybox{<br /> \xymatrix{<br /> {E}\ar[r]^{i} \ar[d]_{f} &amp; {X} \ar[dl]^{f&#039;}\\<br /> {Y} &amp;}}<br /> \end{xy}<br /> \end{displaymath}<br />
the entension of function f;
(i is an inclusion map)

\begin{displaymath}<br /> \begin{xy}<br /> *!C\xybox{<br /> \xymatrix{<br /> {E}\ar[r]^{i} \ar[dr]_{f&#039;} &amp; {X} \ar[d]^{f}\\<br /> &amp;{Y} }}<br /> \end{xy}<br /> \end{displaymath}<br />
the restriction of function f;
(i is an inclusion map)

\begin{displaymath}<br /> \begin{xy}<br /> *!C\xybox{<br /> \xymatrix{<br /> &amp;{E}\ar[d]^{p}\\<br /> {X}\ar[ur]^{f&#039;}\ar[r]_{f} &amp; {Y} } }<br /> \end{xy}<br /> \end{displaymath}<br />
the lifting of function f;

then how do we call the function f' in this this diagram:
\begin{displaymath}<br /> \begin{xy}<br /> *!C\xybox{<br /> \xymatrix{<br /> {X}\ar[r]^{f}\ar[rd]_{f&#039;} &amp; {Y} \ar[d]^{p}\\<br /> &amp;{E} } }<br /> \end{xy}<br /> \end{displaymath}<br />

 

[navigator]

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.