How can I draw a big equality in a commutative diagram with extensions?

Question

Here is the figure I want to draw:

I know how to draw a commutative square, like this:

\[\begin{tikzcd}[sep = large]
0 \ar[r] & A \ar[d]\ar[r] & B  \ar[d]\ar[r] & C \ar[d]\ar[r] & 0 & (a) \\
0 \ar[r] & X \ar[d]\ar[r] & Y \ar[d]\ar[r] & Z \ar[d]\ar[r] & 0 & (b)\\
\end{tikzcd}\]

How can I add a big equality sign instead of an arrow and how can I start from the bottom by the sequence given in my picture?

Answer 1

Already in TikZ there is a key double equal sign distance which allows you to draw double lines with the appropriate distance between the lines.

\documentclass{article}
\usepackage{amsmath}
\usepackage{tikz-cd}
\begin{document}
\[\begin{tikzcd}[sep = large]
 & & \Sigma M\ar[r,-,double equal sign distance,double] 
 \arrow[d,"f"']& \Sigma M \arrow[d,"\text{pinch}"]& & \\
 M\vee M \vee M \ar[r,"{(\lambda_1,\lambda_2,\lambda_3)}"]& N \arrow[r]&
 X \arrow[r]& \Sigma M\vee\Sigma  M \vee\Sigma  M\\
\end{tikzcd}\]
\end{document}

Answer 2

With another alignment of the rightmost vertical arrow, thanks to mathtools:

\documentclass{article}
\usepackage{tikz-cd, mathtools}
\begin{document}
\begin{tikzcd}[column sep=large, row sep=huge]
 & & \Sigma M \dar["f", swap]\rar[equal]& \Sigma M \dar["\text{pinch}"]\\
 M\vee M\vee M\rar{(\lambda_1,\lambda_2, \lambda_3)} & N \rar & X \rar& \Sigma M\vee\mathrlap{\Sigma M\vee \Sigma M}
\end{tikzcd}


\end{document} 

Answer 3

Add the option equal for the arrow.

However, the diagram is very wide already with standard column separation, so using sep=large will make it too wide.

I suggest to widen only the first arrow in the bottom row which can be accomplished with &[2em] in the first row. Using row sep=large will somehow balance the whole thing.

\documentclass{article}
\usepackage{amsmath}
\usepackage{tikz-cd}
\begin{document}
[
\begin{tikzcd}[row sep = large]
% top row
  &[2em] % some more length for the first arrow
  &
  \Sigma M \arrow[r,equal] \arrow[d,"f"'] &
  \Sigma M \arrow[d,"\mathrm{pinch}"]
\
% bottom row
  M \vee M \vee M \arrow[r,"{(\lambda_1,\lambda_2,\lambda_3)}"] &
  N \arrow[r] &
  X \arrow[r] &
  \Sigma M \vee \Sigma M \vee \Sigma M
\end{tikzcd}
]
\end{document}