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