[Tex/LaTex] Commutative diagram with curved arrow

Question

I want to get a bent arrow from node A to node E, this is my code:

\usepackage{tikz-cd}
\usetikzlibrary{cd}
\usepackage{tikz}
\usetikzlibrary{positioning}

\begin{document}

\begin{center}
\begin{tikzpicture}

\node (E) at (0,0) {$T_V U$};
\node[right=of E] (F) {$U\times V$};
\node[below=of F] (A) {$U$};
\node [right=of F] (D) {};
\node [below=of D] (G) {$V$};


\draw[->] (E)--(F) node [midway,above] {$\simeq$};
\draw[->] (E)--(A) node [midway,below] {$f$};
\draw[->] (F)--(A) node [midway,right] {$\pi^2$};
\draw[->] (F)--(G) node [midway,right] {$\pi^1$};
\draw[->,bend] (A)--(E) node [midway,left] {$v$}


\end{tikzpicture}
\end{center}

\end{document}

Answer 1

I suggest using tikz-cd directly:

\documentclass{article}
\usepackage{tikz-cd}

\begin{document}

\[
\begin{tikzcd}
T_V U \arrow [dr,"f"] \arrow[r,"\simeq"] &
  U\times V \arrow[d,"\pi^2"] \arrow[dr,"\pi^1"] \\
& U \arrow[ul,bend left,"v"] & V
\end{tikzcd}
\]

\end{document}