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?

user242026 · Accepted Answer

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 Mar[r,-,double equal sign distance,double] 
 arrow[d,"f"']& Sigma M arrow[d,"text{pinch}"]& & 
 Mvee M vee M ar[r,"{(lambda_1,lambda_2,lambda_3)}"]& N arrow[r]&
 X arrow[r]& Sigma MveeSigma  M veeSigma  M
end{tikzcd}]
end{document}

Bernard · Answer

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}"]
     Mvee Mvee Mrar{(lambda_1,lambda_2, lambda_3)} & N rar & X rar& Sigma Mveemathrlap{Sigma Mvee Sigma M}
    end{tikzcd}

end{document}

egreg · Answer

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}

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

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