\documentclass[10pt]{article}
\usepackage[usenames]{color} %used for font color
\usepackage{amssymb} %maths
\usepackage{amsmath} %maths
\usepackage[utf8]{inputenc} %useful to type directly diacritic characters
\usepackage{tikz-cd}\begin{document}
\begin{tikzcd}
{\rm rank}_1 [\mathcal{M}(\Omega_1 \times \Omega_2) ] \ar[r,"Y_*"] \ar[d,"X_*"] & \mathcal{M}(\Omega_2) \\
\mathcal{M}(\Omega_1) & \mathcal{M}(\Omega_1) \times \mathcal{M}(\Omega_2)
\ar[u] \ar[l] \ar[ul,"\otimes"]
\end{tikzcd}
\end{document}