Arrows for morphisms of exact sequences

Question

I'm trying to figure out a good way to use LaTeX to draw the following diagram (snapshot image from a document).

The closest I could come to this is using the following code:

\begin{align}
\begin{array}{ccccccccc}
  0 &\xlongrightarrow & M' & \xlongrightarrow & M & \xlongrightarrow & M'' & \xlongrightarrow & 0\\
  & & \bigg\downarrow & & \bigg\downarrow & & \bigg\downarrow & & \\
  0 &\xlongrightarrow & N' & \xlongrightarrow & N & \xlongrightarrow & N'' &  \xlongrightarrow & 0
\end{array}
\end{align}

which renders to the following picture:

Using the array and align environment does not seem like a good thing to do. Is there a more efficient way to make such a diagram with arrows? I have seen similar posts which suggest TikZ, but I don't know much about it -- maybe I'll learn it. But multiple solutions or pointers in the right direction will be very welcome.

What about arrows at angles (say something from $M'$ in the first row to $N$ in the second row -- it makes no sense in the context here, but I'd like to be able to make such arrows easily, with little modification to the code needed in case of changes)?

Answer 1

If you like a TikZ solution (with also the diagonal arrow):

\documentclass{article}
\usepackage{tikz-cd}
\begin{document}
    \begin{tikzcd}%
        0 \arrow[r] & M' \arrow[r] \arrow[d] \arrow[rd] & M \arrow[r]  \arrow[d] & M'' \arrow[r] \arrow[d]  & 0 \\  
        0 \arrow[r] & N' \arrow[r]  & N \arrow[r]  & N'' \arrow[r]  & 0 
    \end{tikzcd}%
\end{document}

Answer 2

Here is a simple solution. The long right arrows are produced with hboxes. You can adapt the length; I chose here 1cm.

\documentclass{article}

\usepackage{amsmath}

\newcommand{\Lrightarrow}{\hbox to1cm{\rightarrowfill}}
\newcommand{\Ldownarrow}{\bigg\downarrow}


\begin{document}

\[
  \setlength{\arraycolsep}{1pt}
  \begin{array}{*{9}c}
    0 &\Lrightarrow & M' & \Lrightarrow & M & \Lrightarrow & M'' & \Lrightarrow & 0\\
    & & \Ldownarrow & & \Ldownarrow & & \Ldownarrow & & \\
    0 &\Lrightarrow & N' & \Lrightarrow & N & \Lrightarrow & N'' &  \Lrightarrow & 0
  \end{array}
\]

\end{document}

Answer 3

Using the amscd package gives similar results, though diagonal arrows are not supported:

\documentclass{article}
\usepackage{amscd}
\begin{document}
\[
\begin{CD}
0 @>>> M' @>>> M @>>> M'' @>>> 0 \\
@. @VVV @VVV @VVV \\
0 @>>> N' @>>> N @>>> N'' @>>> 0
\end{CD}
\]
\end{document}

Answer 4

Here is a solution using the xy-pic package, including a diagonal arrow:

\documentclass{article}
\usepackage[all]{xy}
\begin{document}
\xymatrix{
0 \ar[r]    & M' \ar[d]\ar[r] \ar[dr]   & M \ar[d]\ar[r]    & M'' \ar[d]\ar[r]  & 0 \\
0 \ar[r]    & N' \ar[r]                 & N \ar[r]          & N'' \ar[r]        & 0
}
\end{document}

XY-pic User's Guide