Set the elements in corners to keep the arrow length same in a tikzcd commutative diagram

Question

In my commutative diagram in my MWE, I want to keep the arrow lengths fixed in such a way that the lengths of elements (math terms or equations) should not affect the individual arrow lengths. Here's my MWE:

\documentclass{report}
\usepackage{amsmath}
\usepackage{tikz-cd}
\begin{document}
$$

\begin{tikzcd}
        \Psi \arrow[d, "\partial_a"]\arrow[r, "U"] & \Psi' \arrow[d, ]\
        \partial_a \Psi \arrow[r, "U"] & (\partial_a\Psi)' = U(\partial_a\Psi)
\end{tikzcd}
$$
\end{document}

I am getting the output as follows:

But my desired output is:

How can I do it?

Answer 1

Here is a code that uses the macros \mathllap and \mathrlap of the package mathtools. It should be useful in several situations.

\documentclass{report}
\usepackage{mathtools}
\usepackage{tikz-cd}
\begin{document}
\section*{KO}
[

\begin{tikzcd}
        \Psi \arrow[d, "\partial_a"]\arrow[r, "U"] & \Psi' \arrow[d, ]\
        \partial_a \Psi \arrow[r, "U"] & (\partial_a\Psi)' = U(\partial_a\Psi)
\end{tikzcd}
]
\section*{OK}
[
\begin{tikzcd}
      \mathllap{\Psi}

            \arrow[d, "\partial_a", shift right=4pt]
            \arrow[r, "U"]
    & \mathrlap{\Psi'}
            \arrow[d, shift left=4pt]
    \
      \mathllap{\partial_a \Psi}
            \arrow[r, "U"]
    & \mathrlap{(\partial_a\Psi)' = U(\partial_a\Psi)}
\end{tikzcd}
]
\section*{Another use}
[
\begin{tikzcd}
      \mathllap{(\partial_a\Psi)' = U(\partial_a\Psi)}

            \arrow[d, "\partial_a", shift right=4pt]
            \arrow[r, "U"]
    & \mathrlap{(\partial_a\Psi)' = U(\partial_a\Psi)}
            \arrow[d, "\partial_a", shift left=4pt]
    \
      \mathllap{\partial_a \Psi}
            \arrow[r, "U"]
    & \mathrlap{(\partial_a\Psi)' = U(\partial_a\Psi)}
\end{tikzcd}
]
\end{document}

The corresponding output.

Answer 2

For the particular case,

\documentclass{report}
\usepackage{amsmath,mathtools}
\usepackage{tikz-cd}
\begin{document}
\noindent X\dotfill X
[
\begin{tikzcd}
  \Psi \arrow[d, "\partial_a"]\arrow[r, "U"] & \Psi' \arrow[d, ]\
  \partial_a \Psi \arrow[r, "U"] & (\partial_a\Psi)'\mathrlap{{} = U(\partial_a\Psi)}
\end{tikzcd}
\hphantom{{} = U(\partial_a\Psi)}
]
\end{document}

The excess part is typeset in a zero width box sticking to the right. The same material is added as a phantom to get centering correct.

Please, be aware that $$ is not good in LaTeX and it has been so since the first release, around 1982 (which makes 40 years or so).

Answer 3

You habe two things you want to solve here:

1. The arrows should have the same length. (Only the horizontal ones?)

   The easiest solution to this is to make all the nodes in each column have the same width.

2. And the right-hand side of one of your cells should not be part of this same width.

   In this simple case, this is easiest achieved with a third column that has no column separation to its predecessor.

For 2. I'm using the key no csep which takes a list of columns that shouldn't have a column separation to their successors. Here, you just want no csep = 2.

For 1. you can use set widest math that is a list of the widest content of each column, here: set widest math={\partial_a \Psi, (\partial_a\Psi)'}.

For other solutions for 2. take a look at another answer of mine where I'll explore some ideas. If handling an extra column is not to your liking that answer's solution 2. and 3. are more appropriate then.

For other solution for 1. you can directly have TikZ measure each node and apply the needed minimum width for it on the next run.

If you don't actually want the column centered, you can actually just use Case 1 of this answer.

---

In the code below, I've commented an arrow that connects the north anchors of the second row's nodes to show that even the vertical arrows are not the same length.

Code

\documentclass{report}
\usepackage{mathtools, tikz-cd}
\tikzcdset{
  no csep/.style={/utils/temp/.style={/tikz/column ##1/.append style={
    column sep=-2*(\pgfkeysvalueof{/pgf/inner xsep})}},/utils/temp/.list={#1}},
  set widest math/.style={
    /utils/exec=\def\pgfmathcounter{0},
    /utils/temp/.code=\edef\pgfmathcounter{\pgfinteval{\pgfmathcounter+1}}%
      \pgfkeysalso{/tikz/column \pgfmathcounter/.append style={
        align=center, text width={width("$##1$")}}},
    /utils/temp/.list={#1}}}
\usepackage[showframe, pass]{geometry}
\begin{document}
\[
\begin{tikzcd}[set widest math={\partial_a \Psi, (\partial_a\Psi)'}, no csep=2]
  \Psi                   \arrow[d, "\partial_a"] \arrow[r, "U"]
& \Psi'                  \arrow[d] \\
  \partial_a \Psi        \arrow[r, "U"]
& (\partial_a\Psi)'
& {} = U(\partial_a\Psi)
%  \ar[help lines, start anchor=north, end anchor=north, l]
\end{tikzcd}
\]
\end{document}

Output

Answer 4

I have used another strategy that is into the code below using \mkern and xshift.

\documentclass[a4paper,12pt]{article}
\usepackage{tikz-cd}
\begin{document}
\begin{tikzcd}[column sep=0pt]
\mkern2mu\Psi \arrow[r, "U",{xshift=4pt}] \arrow[d, "\partial_a"] &    \Psi' \arrow[d] \\
\partial_a \Psi \arrow[r, "U",end anchor={[xshift=6.67em]}]{r}   & \mkern115mu  (\partial_a\Psi)' = U(\partial_a\Psi)
\end{tikzcd}
\end{document}