\node (E) at (0,0) {$E|_U:=\pi^{-1}(U)$};
\node[right=of E] (F) {$U\times F$};

\draw[->] (E)--(F) node [midway,above] (phi) {$\Phi$};
\node[below= 1cm of phi] (A) {$U$};
\draw[->] (E)--(A.north west) node [midway,below] {$\pi$};
\draw[->] (F)--(A.north east) node [midway,right] {$\pi_1$};
\draw [<-] ([yshift=2mm]A.north) arc[start angle=-90,delta angle=270,radius=0.25cm];

  • please edit your code so that it's compilable wthout guesswork.
    – Mico
    Oct 31 '15 at 7:59

Would have been nice if you mentioned that you have tikz-cd code for the diagram from a previous question.

tikz-cd makes a matrix of nodes that the elements are placed in. By adding every matrix/.append style={name=M} you can use M-m-n to refer to a specific cell, where m is row number and n is column number (or vice versa, I can never remember). Then you can use execute at end picture to draw the arrow relative to the bottom middle cell.

enter image description here

\begin{tikzcd}[every matrix/.append style={name=m},
  execute at end picture={
        \draw [<-] ([yshift=2mm]m-2-2.north) arc[start angle=-90,delta angle=270,radius=0.25cm];
   E|_U:=\pi^{-1}(U)\arrow[rr,"\Phi" ]\arrow[dr,swap,"\pi" ]& & U\times \mathbb{R}^k \arrow[dl,"\pi_1" ] \\
      &  U &

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