Welcome! tikz-cd allows you to draw such diagrams. I am sure I did not decipher everything (just because some glyphs are ambiguous) but you will probably find it easy to edit this code.

\documentclass{article}
\usepackage{amsmath}
\usepackage{dsfont}
\usepackage{tikz-cd}
\begin{document}
\begin{tikzcd}[row sep=2em,column sep=2.5em]
 I\times I \arrow[drr,"\text{respect equivalence $\sim$}",bend left] 
  \arrow[dr,"\text{stretch}",bend left] \arrow[d,"q"] & & \\
 M_* \arrow[drr,"\exists!m",bend right]  & [0,2\pi]\times[-1,1] \arrow[r,"\bar u"] & \mathds{R}^3\\
 & & M \arrow[u,"\cap_H"']\\
\end{tikzcd}
\end{document}

Welcome! tikz-cd allows you to draw such diagrams. I am sure I did not decipher everything (just because some glyphs are hard to read) but you will probably find it easy to edit this code.

\documentclass{article}
\usepackage{amsmath}
\usepackage{dsfont}
\usepackage{tikz-cd}
\begin{document}
\[\begin{tikzcd}[row sep=2em,column sep=2.5em]
 I\times I \arrow[drr,"\text{respect equivalence $\sim$}",bend left] 
  \arrow[dr,"\text{stretch}",bend left] \arrow[d,"q"] & & \\
 M_* \arrow[drr,"\exists!m",bend right]  & {}[0,2\pi]\times[-1,1] \arrow[r,"\bar u"] & \mathds{R}^3\\
 & & M \arrow[u,"\cap_H"']\\
\end{tikzcd}\]
\end{document}