Tags for rows in a commutative diagram using tikz-cd

Question

Consider a commutative diagram such as

\documentclass{scrartcl}
\usepackage{mathtools, tikz-cd}
\begin{document}
    \begin{equation}
        \begin{tikzcd}
            0 \rar & A \dar \rar & B \dar \rar & C \dar \rar & 0 &[3em] \text{(\textit{i})}\\
            0 \rar & A' \rar & B' \rar & C' \rar & 0 & \text{(\textit{ii})}
        \end{tikzcd}
    \end{equation}
\end{document}

As you can see, I'd like to add labels to the rows of the diagram. Now, you'll agree that this solution is rather ugly. Is it possible to add labels to the rows that appear at the margin; i.e., instead of what you see, I'd like to have, e.g., Which I produced using

\documentclass{scrartcl}
\usepackage{mathtools, amsmath, tikz-cd}
\tikzset{every picture/.append style={remember picture}}
\begin{document}
    \begin{gather}
        \begin{tikzcd}[ampersand replacement=\&]
            0 \rar \& |[alias=A]|  A \rar \& B \rar \& C \rar \& 0
        \end{tikzcd}\\
        \begin{tikzcd}[ampersand replacement=\&]
            0 \rar \& A' \ar[from=A] \rar \& B' \rar \& C' \rar \& 0 
        \end{tikzcd}
    \end{gather}
\end{document}

which is certainly not the way to go, since it is not particularly stable, and the proper alignment of the cells, which I was too lazy fore here, will be a mess.

Answer 1

You don't really need tikz-cd for this kind of diagrams. Here is a way to do it with alignatand \rotatebox.

Unrelated: you don't have to load amsmath when you load mathtools, since the latter does it for you.

\documentclass{scrartcl}
\usepackage{mathtools}

\begin{document}

    \begin{alignat}{4}
            0 \xrightarrow{\hskip 2em}{} & A & \xrightarrow{\hskip 2em} {}& B & \xrightarrow{\hskip 2em}{} & C \xrightarrow{\hskip 2em} 0 \\[-1ex]
                             & \,\rotatebox[origin=c]{-90}{${} \xrightarrow{\hskip 2em}{}$} & & \,\rotatebox[origin=c]{-90}{${} \xrightarrow{\hskip 2em}{}$} & & \,\rotatebox[origin=c]{-90}{${} \xrightarrow{\hskip 2em}{}$} \notag \\[-1ex]
            0\xrightarrow{\hskip 2em}{} & A' &\xrightarrow{\hskip 2em} {}& B' & \xrightarrow{\hskip 2em}{} & C' \xrightarrow{\hskip 2em} 0
    \end{alignat}

\end{document} 

Answer 2

If the problem of your second example is only the alignment, you can fix it.

This way, there is no problem when you reference the lines:

\documentclass{scrartcl}
\usepackage{mathtools, tikz-cd}
\tikzset{every picture/.append style={remember picture}}
\begin{document}
If the problem of your second example is only the alignment, you can fix it. 

This way, there is no problem referencing the first
\eqref{eq:first} or the second line \eqref{eq:second}:

\begin{gather}
    \begin{tikzcd}[ampersand replacement=\&,
    every cell/.append style={text centered}]
        0 \rar \& |[alias=A, text width=width("$A'$")]|A \rar \& |[text width=width("$B'$")]|B \rar \& |[text width=width("$C'$")]|C \rar \& 0\label{eq:first}
    \end{tikzcd}\\[5ex]
    \begin{tikzcd}[overlay, ampersand replacement=\&]
        0 \rar \& A' \ar[from=A] \rar \& B' \rar \& C' \rar \& 0\label{eq:second} 
    \end{tikzcd}
\end{gather}
\end{document}

Answer 3

This is more of a proof-of-concept since I'm not very familiar with the internals of AMSMath.

Note:

• This needs a node in column 1 for each row.
• If you shift this node up or down, the equation number will move with it vertically.
• The macros \tag and \nonumber won't work.
• The equation number will not be shifted down when the row is too long.
• Don't write anything before or after the TikZ-CD. The placement of the equation numbers are dependent of the diagram being in the horizontal middle of the line.
• Hyperref? Cleveref? Maybe.

Code

\documentclass{scrartcl}
\usepackage{mathtools, tikz-cd}
\makeatletter
\tikzcdset{
  eqno per line/.style={
    /tikz/column 1/.append code=%
      \global\pgfutil@namelet{tikzcd@rowlabel@\the\pgfmatrixcurrentrow}
                             {pgfutil@empty},
    /tikz/execute at end picture={%
      \pgfmathloop % simpler than \foreach
        \node[overlay,path only,anchor=base east,inner sep=+0pt,outer sep=+0pt](@)
        at(.5\linewidth,0|-\tikzcdmatrixname-\pgfmathcounter-1.base){%
          \@eqnswtrue\make@display@tag
          \expandafter\pgfutil@ifxempty
            \csname tikzcd@rowlabel@\pgfmathcounter\endcsname{}{%
            \expandafter\expandafter\expandafter\ltx@label
            \expandafter\expandafter\expandafter{%
              \csname tikzcd@rowlabel@\pgfmathcounter\endcsname}}};%
      \ifnum\pgfmathcounter<\pgfmatrixcurrentrow
      \repeatpgfmathloop}},
  every matrix/.append code={%
    \def\label##1{%
      \expandafter\xdef
        \csname tikzcd@rowlabel@\the\pgfmatrixcurrentrow\endcsname{##1}}}}
\makeatother
\newenvironment*{tikzcdeq}[1][]
  {\begin{equation*}\tikzcd[eqno per line,#1]}
  {\endtikzcd\end{equation*}}
\begin{document}
Lorem \ref{label3}
\begin{equation}
c^2 = a^2 + b^2
\end{equation}
ipsum \ref{label1}
\begin{equation*}
\begin{tikzcd}[eqno per line]
  0 \rar & A \dar \rar & B \dar \rar & C \dar \rar & 0 \label{label1} \\
  0 \rar & A' \rar     & B' \rar     & C' \rar     & 0 \label{label2}
\end{tikzcd}
\end{equation*}
dolor \eqref{label2}
\begin{equation}
E = mc^2
\end{equation}
sit \eqref{label4}
\begin{tikzcdeq}
  0 \rar & A \dar \rar & B \dar \rar & C \dar \rar & 0 \label{label3} \\
  0 \rar & A' \rar     & B' \rar     & C' \rar     & 0 \label{label4}
\end{tikzcdeq}
amet.
\end{document}

Output