\documentclass{standalone}
\usepackage[utf8x]{inputenc}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{newtxtext}
\usepackage[libertine]{newtxmath}

\usepackage{tikz-cd}

\begin{document}

\begin{tikzcd}[row sep=large]
X  \arrow[r, "\phi"] \arrow[rd, "f"] &  U(A)  \arrow[d, dashed, "U(g)" ]           & A \arrow[d, dashed, "g" ]           \\
                                     &  U(Y)                                       & Y                                   \\
\end{tikzcd}
\end{document}