Can't draw a commutative diagram

Here's one possible solution for the lower part using both xy and tikz-cd:

\documentclass{article}
\usepackage[all]{xy}
\usepackage{tikz-cd}

\begin{document}

$\xymatrix{
& S \ar[ld]^{\pi_{i}} \ar[rd]_{\pi_{j}} &\\
R_{i} \ar[rr]_{\mu_{ji}} & & R_{j} }$

\begin{tikzcd}[column sep=normal]
& S \arrow{dl}{\pi_{i}}\arrow{dr}[swap]{\pi_{j}} & \\
R_{i} \arrow{rr}[swap]{\mu_{ji}} & & R_{j}
\end{tikzcd}

\end{document}

Here's the complete diagram using tikz-cd:

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

\begin{document}

\begin{tikzcd}[column sep=normal,row sep=large]
& Y\arrow{ddl}[swap]{\psi_{i}}\arrow{ddr}{\psi_{j}}\arrow{d}{h} & \\
& S \arrow{dl}{\pi_{i}}\arrow{dr}[swap]{\pi_{j}} & \\
R_{i} \arrow{rr}[swap]{\mu_{ji}} & & R_{j}
\end{tikzcd}

\end{document}

And now using xy:

\documentclass{article}
\usepackage[all]{xy}

\begin{document}

$\xymatrix{
& Y\ar[ldd]_{\psi_{i}}\ar[rdd]^{\psi_{j}}\ar[d]^{h} & \\
& S \ar[ld]^{\pi_{i}} \ar[rd]_{\pi_{j}} & \\
R_{i} \ar[rr]_{\mu_{ji}} & & R_{j} }$

\end{document}

And now, as requested in a comment, with some arrows curved:

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

\begin{document}

\begin{tikzcd}[column sep=normal,row sep=large]
& Y\arrow[bend right]{ddl}[swap]{\psi_{i}}\arrow[bend left]{ddr}{\psi_{j}}\arrow{d}{h} & \\
& S \arrow{dl}{\pi_{i}}\arrow{dr}[swap]{\pi_{j}} & \\
R_{i} \arrow{rr}[swap]{\mu_{ji}} & & R_{j}
\end{tikzcd}

\end{document}

And with xy:

\documentclass{article}
\usepackage[all]{xy}

\begin{document}

$\xymatrix{
& Y\ar@/_/[ldd]_{\psi_{i}}\ar@/^/[rdd]^{\psi_{j}}\ar[d]^{h} & \\
& S \ar[ld]^{\pi_{i}} \ar[rd]_{\pi_{j}} & \\
R_{i} \ar[rr]_{\mu_{ji}} & & R_{j} }$

\end{document}

Here a solution with tkz-graph

  \documentclass[11pt]{scrartcl}
  \usepackage{tkz-graph}

  \begin{document}
  \begin{tikzpicture}[scale=5,rotate=-30,->,>=latex,auto] 
  % vertices
     \SetVertexMath  % use math mode for vertex
     \GraphInit[vstyle=Empty] % Nodes are not drawn
     \Vertex{X} % add a vertex at (0,0)
     \Vertices{circle}{X_i,Y,X_j}   % three nodes on a circle
  %edges 

   \Edge[label=$\pi_j$](X)(X_j)   
   \Edge[label=$\Psi_i$,style={bend left}](Y)(X_i) 
   \Edge[label=$u$](Y)(X)  

  \begin{scope}[EdgeStyle/.append style={swap}] % swap labels
   \Edge[label=$\pi_i$](X)(X_i)  
   \Edge[label=$\Psi_j$,style={bend right}](Y)(X_j)
   \Edge[label=$f_{ij}$](X_j)(X_i)
  \end{scope}

  \end{tikzpicture}
  \end{document}