How can I draw this diagram in Latex

Question

Here is the picture of the diagram:

How can I draw this diagram in Latex?

Answer 1

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}

Answer 2

Welcome, there are many different ways to write this diagram with TikZ. Here, I use the matrix library that was written to align the nodes of a diagram.

\documentclass[border=5mm]{article}
\usepackage{amssymb}
\usepackage{tikz}
\usetikzlibrary {matrix}
\begin{document}
\begin{tikzpicture}
\matrix [matrix of math nodes,column sep=1.2cm,row sep=1cm]
{
|(I2)| I\times I    &                               & \\
|(Me)|M_*           & |(X)| [0,2\pi]\times[-1,1]    & |(R)| \mathbb{R}^3 \\
                    &                               & |(M2)| M \\
};
\begin{scope}[every node/.style={midway,auto,font=\scriptsize}]
\draw [->] (I2) -- node {$q$} (Me);
\draw [->](X) -- node {$\bar u$} (R);
\draw [->](I2) to [bend left] node{stretch}(X);
\draw [->](I2) to [bend left] node{respect equiv. $\sim$}(R);
\draw [->](Me) to [bend right] node{$\exists !m$}(M2);
\draw [->](M2) --node[right]{$\cap_M$}(R);
\end{scope}
\end{tikzpicture}
\end{document}

Answer 3

Here's an alternative using xy.

\documentclass[border=5mm]{standalone}
\usepackage[all]{xy}
\usepackage{amssymb} % for the blackboard bold symbol
\usepackage{amsmath} % for \text
\begin{document}
\xymatrix{
    I \times I 
    \ar[d]^{q}
    \ar@/^/[dr]^{\text{stretch}}
    \ar@/^20pt/[drr]^{\strut\text{respect equivalence}\thinspace\sim}
    \\
    M_* 
    \ar@/_12pt/[drr]_{\exists!m} 
    & 
    [0, 2\pi] \times [-1, 1] 
    \ar[r]^-{\bar{u}} 
    & 
    \mathbb{R}^3 
    \\
    &
    & 
    M \ar[u]_{{}\cap_M}
    \\
}
\end{document}

Answer 4

The dot lanquage from graphviz is a great for drawing commutative diagrams as you can see here : commutative diagram

One can use dot language from graphviz, the Python script dot2tex to convert into LaTeX and the dot2texi.sty package to include the dot code into a LaTeX document.

\documentclass{article}
\usepackage{tikz} 
\usetikzlibrary{shapes,arrows} 
\usepackage{dot2texi}
\usepackage{amsmath,amssymb} 
\begin{document}

 \begin{dot2tex}[dot] 
  digraph T 
  {rankdir=TB;   
   ranksep=.2;  
   nodesep=.1  ;
   node [shape=none];
   1 -> 4 [dir=backward xlabel="q   "];
   1 -> 5 [label="stretch" constraint=false];
   1 -> 6 [label="respect equiv. ~ " texlbl="respect equiv. $\sim$" tailport=e headport=no constraint=false];
   4 -> 9 [constraint=false label="∃!m" texlbl="$\exists!m$"];
   5 -> 6 [constraint=false label="μ " texlbl="$\bar\mu$"] ;
   6 -> 9 [dir=back label="∩_M " texlbl="$\cap_M$"];
   1 [label="I x I" texlbl="$I\times I$"];  
   {rankdir=LR ;   rank=same 
   4 [label="M*"];
   5 [label="[0,2Π]✕[-1,1]" texlbl="$[0,2\pi]\times[-1,1]$"];
   6 [label= "R^3" texlbl="$\mathbb{R}^3$"];   }
   9 [label="M"]; }

   \end{dot2tex}
  \end{document}

my emacs source file

The tikzpicture environment created

dot2texi is a great package and can be used to produce very quickly a lot of diagrams in a declarative style.

Answer 5

Another way with plain TikZ: the firuge is just one \path attaching with four nodes and connecting with arrows. The code is long and easy to read.

\documentclass{article}
\usepackage{tikz,amsmath,amssymb,lipsum}
\begin{document}
\lipsum[1]
Define $\bar\mu\colon [0,2\pi]\times [-1,1]\to \mathbb{R}^3$ with some formular as $\mu$.   
\[
\begin{tikzpicture}
\path
(0,0) node (I) {$I\times I$}
++(-90:1.2) node (M1) {$M_*$}
++(0:3) node (M2) {$[0,2\pi]\times [-1,1]$}
++(0:2.5) node (M3) {$\mathbb{R}^3$}
++(-90:1.2) node (M4) {$M$}
;
\begin{scope}[->,nodes={midway,scale=.8}]
\draw (I)--(M1) node[left]{$q$};
\draw (I) to[out=0,in=120] node[above right]{stretch} (M2);
\draw (I) to[out=20,in=120] node[above right]{respect equivalence $\sim$} (M3);
\draw (M1) to[out=-50,in=-160] node[above]{$\exists ! m$} (M4);
\draw (M2)--(M3) node[above]{$\bar\mu$};
\draw (M4)--(M3) node[right]{\rotatebox[origin=c]{270}{$\subseteq$}$_\mu$};
\end{scope}
\end{tikzpicture}
\]
\lipsum[1]
\end{document}