How can I draw this diagram about tensor product?

Question

How can I draw besser with tikz-pgf this diagram in LaTeX?

UPDATE - 06.04.2017 - 02:17 : Why -2? I don´t understand! I can´t use tikz-pgf, I´m not expert and I ask for help! What kind of MWE do you want? I tried and my result is following:

\documentclass{article}
\usepackage[fontsize=9]{scrextend}
\usepackage[german]{babel}
\usepackage{blindtext}
\usepackage{lmodern}
\usepackage{color}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{amssymb}
\usepackage{latexsym}
\usepackage{amsmath}
\usepackage{amsthm}
\usepackage{dsfont}
\usepackage{mathrsfs}
\usepackage{wasysym}
\usepackage{marvosym}
\usepackage{graphicx}
\usepackage{blindtext}
\usepackage{tabularx}
\usepackage{tabulary}
\usepackage{booktabs}
\usepackage{wasysym}
\usepackage[usestackEOL]{stackengine}
\usepackage[cal=rsfso]{mathalfa}
\usepackage[a4paper,top=1cm,bottom=2cm,left=1.5cm,right=2cm]{geometry}
\usepackage{tipa}
\usepackage{amscd}
\usepackage{amstext}
\usepackage{marvosym}
\usepackage{hyperref}
\usepackage{tikz-cd}
\begin{document}
\begin{tikzcd}
V_1^{(1)} \otimes \cdots \otimes V_{k_1}^{(1)} \otimes \cdots \otimes 
V_1^{(l)}\otimes \cdots \otimes V_{k_l}^{(l)} \arrow[rd]  &  \\
& (V_1^{(1)} \otimes \cdots \otimes V_{k_1}^{(1)}) \otimes \cdots \otimes 
(V_1^{(l)}\otimes \cdots \otimes V_{k_l}^{(l)})  \\
& (V_1^{(1)} \otimes \cdots \otimes V_{k_1}^{(1)}) \times \cdots \times 
(V_1^{(l)}\otimes \cdots \otimes V_{k_l}^{(l)}) \arrow[u] \\
V_1^{(1)} \times \cdots \times V_{k_1}^{(1)} \times \cdots \times 
V_1^{(l)}\times \cdots \times V_{k_l}^{(l)} \arrow[ru] 
\end{tikzcd}
\end{document}

UPDATE - 06.04.2017 - 06:25 :In addition, I used LatexDraw and with XeLaTex I have:

\documentclass{article}
\usepackage[fontsize=9]{scrextend}
\usepackage[german]{babel}
\usepackage{blindtext}
\usepackage{lmodern}
\usepackage{color}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{amssymb}
\usepackage{latexsym}
\usepackage{amsmath}
\usepackage{amsthm}
\usepackage{dsfont}
\usepackage{mathrsfs}
\usepackage{wasysym}
\usepackage{marvosym}
\usepackage{graphicx}
\usepackage{blindtext}
\usepackage{tabularx}
\usepackage{tabulary}
\usepackage{booktabs}
\usepackage{wasysym}
\usepackage[usestackEOL]{stackengine}
\usepackage[cal=rsfso]{mathalfa}
\usepackage[a4paper,top=1cm,bottom=2cm,left=1.5cm,right=2cm]{geometry}
\usepackage{tipa}
\usepackage{amscd}
\usepackage{amstext}
\usepackage{marvosym}
\usepackage{hyperref}
\usepackage{tikz-cd}
\usepackage[pdf]{pstricks}
%\usepackage[usenames,dvipsnames]{pstricks}
\usepackage{epsfig}
\usepackage{pst-grad} % For gradients
\usepackage{pst-plot} % For axes
\usepackage[space]{grffile} % For spaces in paths
\usepackage{etoolbox} % For spaces in paths
\makeatletter % For spaces in paths
\patchcmd\Gread@eps{\@inputcheck#1 }{\@inputcheck"#1"\relax}{}{}
\makeatother
\begin{document}
% 
\psscalebox{1.0 1.0} % Change this value to rescale the drawing.
{
\begin{pspicture}(0,-5.055)(11.07,5.055)
\rput(3.14,4.8){$V_1^{(1)} \otimes \cdots \otimes V_{k_1}^{(1)} \otimes 
\cdots \otimes 
V_1^{(l)}\otimes \cdots \otimes V_{k_l}^{(l)}$}
\rput(7.54,1.6){$\left ( V_1^{(1)} \otimes \cdots \otimes V_{k_1}^{(1)} 
\right )  \otimes \cdots \otimes 
\left (V_1^{(l)}\otimes \cdots \otimes V_{k_l}^{(l)} \right )$}
\rput(7.54,-1.6){$\left ( V_1^{(1)} \otimes \cdots \otimes V_{k_1}^{(1)} 
\right )  \times \cdots \times 
\left (V_1^{(l)}\otimes \cdots \otimes V_{k_l}^{(l)} \right )$}
\rput(3.14,-4.8){$ V_1^{(1)} \times \cdots \times V_{k_1}^{(1)} \times 
\cdots \times 
V_1^{(l)}\times \cdots \times V_{k_l}^{(l)} $}
\psline[linecolor=black, linewidth=0.02, arrowsize=0.053cm 
1.5,arrowlength=1.4,arrowinset=0.0]{->}(3.54,4.4)(7.54,2.0)
\psline[linecolor=black, linewidth=0.02, arrowsize=0.053cm 
1.5,arrowlength=1.4,arrowinset=0.0]{->}(7.49,-1.1)(7.49,1.15)
\psline[linecolor=black, linewidth=0.02, arrowsize=0.053cm 
1.5,arrowlength=1.4,arrowinset=0.0]{->}(3.54,-4.4)(7.54,-2.0)
\psbezier[linecolor=black, linewidth=0.02, linestyle=dashed, 
dash=0.17638889cm 0.10583334cm, arrowsize=0.053cm 
1.5,arrowlength=1.4,arrowinset=0.0]{->}(3.14,-4.4)(1.94,-2.0)(3.94,0.0)
(4.34,1.2)
\psbezier[linecolor=black, linewidth=0.02, arrowsize=0.053cm 
1.5,arrowlength=1.4,arrowinset=0.0]{->}(2.74,-4.4)(-1.26,-2.0)(2.74,1.2)
(3.14,4.4)
\rput(7.14,-3.2){$\otimes ^{(1)} \times \cdots  \times \otimes^{(k)} $}
\rput{2.3059666}(0.0064297295,-0.31947264){\rput(7.94,0.0){$\otimes$}}
\rput{2.3059666}(0.017017499,-0.04554495){\rput(1.14,0.4){$\otimes$}}
\rput{68.87306}(0.633066,-3.323306){\rput(2.74,-1.2){$\otimes \circ \left 
(\otimes ^{(1)}, \cdots  ,\otimes^{(k)} \right )$}}
\rput{2.3059666}(0.14933528,-0.21999136){\rput(5.54,3.6){$a$}}
\end{pspicture}
}
%
\end{document}

Answer 1

Here a MWE for showing the basic commands needed to achieve what you want.

I think the commands are self-explanatory, in doubt see the great pgfmanual with it's detailed examples that cover everything to get started with tikz.

\documentclass[tikz, border=5mm]{standalone}

\usetikzlibrary{positioning}

\begin{document}
  \begin{tikzpicture}
    \node (first) {$V_{1}^{(1)} \otimes\cdots\otimes V_{k_1}^{(1)} \otimes\cdots\otimes$};
    \node (second) [below=2 of first] {$V_{1}^{(1)} \times\cdots\times V_{k_1}^{(1)} \times\cdots\times$};
    \node (third) [below right=.75 of first] {$\left(V_{1}^{(1)\otimes\cdots\otimes}V_{k_1}^{(1)} \right)\otimes\cdots\otimes$};

    \begin{scope}[->]
        \draw (first) to node [midway, above] {a} (third);
        \draw (second) to [out=120, in=270] node [midway, above, sloped] {$\otimes$} (first) ;
        \draw [dashed] (second) to [in=180] node [midway, above, sloped] {$\otimes (\otimes^{(1)},\dots)$} (third);
    \end{scope}
  \end{tikzpicture}
\end{document}

Answer 2

Regarding the lines with text, this can be achieved with two features of tikt/pgf (I refer to the tikz/pgf manual with the version 3.0.1a).

17.8 Placing Nodes on a Line or Curve Explicitly

17.13 Referencing Nodes Outside the Current Picture

Especially 17.13.1 Referencing a Node in a Different Picture.

Here's an example that is somehow similar to your wish.