Tikz matrix arrows alignment

Question

I have a problem that I cannot solve for myself.

The following code produces the following image, which I do not really like.

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{matrix, arrows}
\usepackage{amssymb}

\begin{document}

\begin{center}
\begin{tikzpicture}
  \matrix (m) [matrix of math nodes, row sep=0em, column sep=4em, minimum width=2em]
  { 0 & \mathbb{Z}\times\mathbb{Z} & \mathbb{Z}^2          & 0 \\
      & (\alpha_0, \alpha_1)       & (-\alpha_0, \alpha_1) &   \\
      &                            & \beta_{01}            & 0 \\ };
\path[>=stealth, ->]
    (m-1-1.east|-m-1-2) edge node [above] {\scriptsize$d_{-1}$} (m-1-2.west|-m-1-2)
    (m-1-2.east|-m-1-2) edge node [above] {\scriptsize$d_{ 0}$} (m-1-3.west|-m-1-2)
    (m-1-3.east|-m-1-2) edge node [above] {\scriptsize$d_{ 1}$} (m-1-4.west|-m-1-2);
\path[>=stealth, |->]
    (m-2-2.east|-m-2-2) edge (m-2-3.west|-m-2-2);
\path[>=stealth, |->]
    (m-3-3.east|-m-3-3) edge (m-3-4.west|-m-3-3);
\end{tikzpicture}
\end{center}


\end{document}

What I want to achieve is having arrows aligned, more or less as in the following image

Does someone have some hint?
I prefer to use tikz, but any other package can be welcome.

Answer 1

Unless you use TiKZ for some other reason. There is no need to use it to obtain your diagram.

With help from "The Comprehensive LaTeX symbols list" (for \xrightarrow and \xmapsto) and egreg's answer to Make box with minimum width (in math mode) (for \minwidthbox) is possible to write:

\documentclass{article}
\usepackage{amsmath,amssymb,empheq,mathtools}

\DeclareRobustCommand{\minwidthbox}[2]{%
  \ifmmode
    \expandafter\mathmakebox
  \else
    \expandafter\makebox
  \fi
  [\ifdim#2<\width\width\else#2\fi]{#1}%
}

\begin{document}

\[
\begin{array}{ccccccc}
0 & \xrightarrow{\minwidthbox{d_{-1}}{3em}}    
   & \mathbb{Z}\times\mathbb{Z}
   & \xrightarrow{\minwidthbox{d_0}{3em}} 
   & \mathbb{Z}^2 
   & \xrightarrow{\minwidthbox{d_1}{3em}} 
   & 0 \\
   &  
   & (\alpha_0,\alpha_1) 
   & \xmapsto{\minwidthbox{}{3em}} 
   & (-\alpha_0,\alpha_1) 
   & 
   & \\
   & 
   & 
   & 
   & \beta_{01} & \xmapsto{\minwidthbox{}{3em}}  & 0 
\end{array}
\]
\end{document}

which produces

Answer 2

Thanks to @percusse for pointing me in the right direction to find the solution.

Styling column by column is a solution to this problem (altought not as elegant as I expected).
The point is to modify each column definition to obtain what I want, so for example

column 2/.style={nodes={text width=1.5cm, align=center}}

The final code is the following

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{matrix, arrows}
\usepackage{amssymb}

\begin{document}

\begin{center}
\begin{tikzpicture}
  \matrix (m) [matrix of math nodes, row sep=0em, column sep=4em, column 2/.style={nodes={text width=1.5cm, align=center}},column 3/.style={nodes={text width=1.5cm, align=center}}]
  { 0 & \mathbb{Z}\times\mathbb{Z} & \mathbb{Z}^2          & 0\\
      & (\alpha_0, \alpha_1)       & (-\alpha_0, \alpha_1) & \\
      &                            & \beta_{01}            & 0\\ };
\path[>=stealth, ->]
    (m-1-1.east|-m-1-2) edge node [above] {\scriptsize$d_{-1}$} (m-1-2.west|-m-1-2)
    (m-1-2.east|-m-1-2) edge node [above] {\scriptsize$d_{ 0}$} (m-1-3.west|-m-1-2)
    (m-1-3.east|-m-1-2) edge node [above] {\scriptsize$d_{ 1}$} (m-1-4.west|-m-1-2);
\path[>=stealth, |->]
    (m-2-2.east|-m-2-2) edge (m-2-3.west|-m-2-2);
\path[>=stealth, |->]
    (m-3-3.east|-m-3-3) edge (m-3-4.west|-m-3-3);
\end{tikzpicture}
\end{center}


\end{document}

Answer 3

You could also define an \Arrow command of fixed width and variable style and let the \matrix manage the alignment and column widths instead of doing it manually:

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{matrix, arrows}
\usepackage{amssymb}

\newcommand{\Arrow}[2][->]{%
    \tikz[baseline=-0.7ex, x=2cm, #1]
        \path (0,0) edge node [above] {\scriptsize#2} (1,0);
}
\begin{document}
\begin{center}
\begin{tikzpicture}
  \matrix (m) [matrix of math nodes, row sep=0em]
  { 0 & \Arrow{$d_{-1}$} & \mathbb{Z}\times\mathbb{Z} & \Arrow{$d_{0}$} & \mathbb{Z}^2          & \Arrow{$d_{1}$} & 0 \\
      &                  & (\alpha_0, \alpha_1)       & \Arrow[|->]{}   & (-\alpha_0, \alpha_1) &                 &   \\
      &                  &                            &                 & \beta_{01}            &  \Arrow[|->]{}  & 0 \\ };
\end{tikzpicture}
\end{center}
\end{document}

Result: