\documentclass[crop,tikz,convert=pdf2svg]{standalone}
\usepackage{tikz}
\colorlet{darkgreen}{green!50!black!100}
\colorlet{darkbrown}{orange!50!black!100}
\begin{document}
\thispagestyle{empty}
\begin{tikzpicture}[x=1.5cm,y=1.5cm]
\foreach \n/\x/\y/\t in {X/0/2/X,Z/2/2/Z,W/4/2/W,TU/6/2/T(U),Y/1/1/Y,V/3/1/V,TY/5/1/T(Y),U/2/0/U,TX/4/0/T(X)} \node (\n) at (\x,\y) {$\t$};
\begin{scope}[->,every node/.style={midway,auto},font=\scriptsize]
\foreach \a/\b/\l in {X/Y/f,Y/U/f'} \draw[blue] (\a) -- node[swap]{$\l$} (\b);
\draw[blue] (U) to [bend right] node[swap]{$f''$} (TX);
\foreach \a/\b/\l in {TX/TY/T(f),TY/TU/T(f')} \draw (\a) -- node[swap]{$\l$} (\b);
\foreach \a/\b/\l in {Y/Z/g,W/TY/g''} \draw[red] (\a) -- node{$\l$} (\b);
\draw[red] (Z) to [bend left] node{$g'$} (W);
\draw[darkgreen] (X) to [bend left] node{$h$} (Z);
\foreach \a/\b/\l in {Z/V/h',V/TX/h''} \draw[darkgreen] (\a) -- node{$\l$} (\b);
\foreach \a/\b/\l in {U/V/j,V/W/j'} \draw[darkbrown] (\a) -- node{$\l$} (\b);
\draw[darkbrown] (W) to [bend left] node{$j''$} (TU);
\end{scope}
\end{tikzpicture}
\end{document}