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What do we call the function in this diagram?

  1. Feb 28, 2009 #1
    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]
     
  2. jcsd
  3. Feb 28, 2009 #2
    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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