Is there a vertical \mapsto symbol?

Question

What is the TeX code for a vertical \mapsto symbol? I've looked but can't find it.

I'm drawing a commutative diagram, and I want to draw what a specific symbol is being mapped to as well, so I am doing this on the label of the vertical arrow, by adjusting the position of the elements of the label. The rest has worked fine, all I need is a vertical \mapsto symbol. The best I can do at the moment is to use \downarrow and put a hyphen slightly above, but that doesn't look great.

\usepackage[all]{xy} 

\xymatrix{
  0 \ar[r] & 
  A_{n+1} \ar[r] \ar[d] &
  B_{n+1} \ar[r] \ar[d] &
  C_{n+1} \ar[r] \ar[d] &
  0 \ar[d]
  \\
  &
  A_n \ar[r] \ar[d] &
  B_n \ar[r] \ar[d]^(0.25){b}^(0.6){d_{n}} &
  C_n \ar[r]^{g_n} \ar[d]_(0.3){c}_(0.44){ \; \; - }_{ \downarrow}_(0.7){0} &
  0 \ar[d]
  \\
  &
  A_{n-1} \ar[r]^(0.2){a} &
  B_{n-1} \ar[r]^{f_{n-1}} &
  C_{n-1} \ar[r] & 0
}

Answer 1

The MnSymbol package offers \upmapsto and \downmapsto:

\documentclass{article}
\usepackage{MnSymbol}

\begin{document}

$\upmapsto\quad\downmapsto$

\end{document}

However, using this package will change some other symbols, and this might be no desirable. In this particular case, since the arrow is needed for a commutative diagram I suggest using the tikz-cd package and its mapsto option for arrows:

\documentclass{article}
\usepackage{tikz-cd}

\begin{document}

\begin{tikzcd}
A \arrow{r}{\psi} \arrow[mapsto,color=red]{d}
& B  \\
C \arrow[mapsto,color=red]{r}[color=blue]{\eta}
& D \arrow[mapsto,color=red]{u}
\end{tikzcd}

\end{document}

Now that an edit has been made to the original question including the desired commutative diagram, here it is using tikz-cd:

\documentclass{article}
\usepackage{tikz-cd}

\newcommand\tikzmark[5][0]{%
  \tikz[overlay,remember picture,baseline] \node [rotate=#1,anchor=base,xshift=#4,yshift=#5] (#2) {$\scriptstyle#3$};}

\begin{document}

\begin{tikzcd}
  0 \arrow{r} & 
  A_{n+1} \arrow{r} \arrow{d} &
  B_{n+1} \arrow{r} \arrow{d} &
  C_{n+1} \arrow{r} \arrow{d} &
  0 \arrow{d}
  \\
  &
  A_n \arrow{r} \arrow{d} &
  \tikzmark{s}{b}{14pt}{-9pt}B_n \arrow{r} \arrow{d}{d_n} &
  \tikzmark{s}{c}{-2pt}{-8pt}\tikzmark{e}{0}{-2pt}{-24pt}\tikzmark[270]{a}{\mapsto}{14pt}{-4pt}
  C_n \arrow{r}{g_n} \arrow{d} &
  0 \arrow{d}
  \\
  &
  A_{n-1} \arrow{r}{a} &
  B_{n-1} \arrow{r}{f_{n-1}} &
  C_{n-1} \arrow{r} & 0
\end{tikzcd}

\end{document}

A variation of \tikzmark was used to position some special characters; in particular, the vertical "downmapsto" arrow was obtained with the rotate=270 option applied to a standard \mapsto

Answer 2

You can rotate the symbol:

\usepackage{graphicx} % for \rotatebox
\usepackage{amsmath}  % for \substack
\newcommand{\downmapsto}{\rotatebox[origin=c]{-90}{$\scriptstyle\mapsto$}\mkern2mu}

and input the relevant arrow as

C_n \ar[r]^{g_n} \ar[d]_{\substack{c\\\downmapsto\\0}} &

The added padding space has been computed by trial and error, so as to ensure good alignment.

Answer 3

This symbol is called U+21A7 in the Unicode. There are many fonts which support that. You can search for possible symbols on your system by clicking here.

With help of this font list, I tried some symbols which were available on my machine (this requires Xe- or LuaLaTeX):

% arara: lualatex

\documentclass{article}
\usepackage{fontspec}
\usepackage{booktabs}
\newcommand{\test}[1]{\texttt{#1} & {\fontspec{#1}\symbol{"21A7}}}

\begin{document}
    \begin{tabular}{lc}
        \toprule
        Font & Example \\
        \midrule
        \test{arialuni.ttf} \\
        \test{code2000.ttf} \\
        \test{dejavusans.ttf} \\
        \test{mathcadunimath.otf} \\
        \test{osifont-2013-04-18.ttf} \\
        \test{quivira.otf} \\
        \test{symbola.ttf} \\
        \bottomrule
    \end{tabular}
\end{document}

This symbol is also described in the package unicode-math under the command \mapsdown. Some possible symbols look like this:

% arara: lualatex

\documentclass{article}
\usepackage{unicode-math}

\begin{document}
    $\mapsdown$\setmathfont{XITS Math}$\mapsdown$\setmathfont{Asana Math}$\mapsdown$\setmathfont{TeX Gyre Pagella Math}$\mapsdown$
\end{document}

Included into your diagram, I would do like the following:

% arara: lualatex

\documentclass{article}
\usepackage{tikz-cd}
\usepackage{mathtools}
\usepackage{unicode-math}

\begin{document}
\begin{tikzcd}[row sep = 8ex]
    0 \arrow{r} & A_{n+1} \arrow{r} \arrow{d} & B_{n+1} \arrow{r} \arrow{d} & C_{n+1} \arrow{r} \arrow{d} & 0 \arrow{d} \\
                & A_n \arrow{r} \arrow{d} & B_n \arrow{r} \arrow{d}{d_n} & C_n \arrow{r}{g_n} \arrow[swap]{d}{\substack{c\\[1.1\jot]\mapsdown\\[1.1\jot]0}} & 0 \arrow{d} \\
                & A_{n-1} \arrow{r}{a} & B_{n-1} \arrow{r}{f_{n-1}} & C_{n-1} \arrow{r} & 0
\end{tikzcd}
\end{document}

Answer 4

Staying with the xy package write

\ar@{|->}[r]

@ always indicate some modification to the arrow. Then, inside the bracket {modification of the tail, the shaft, the head}

But if in the bracket, there is only one symbol, ex

 \ar@{|}[r]

it will modify the head.

cf.ftp://ctan.unsw.edu.au/tex-archive/macros/generic/diagrams/xypic/xy/doc/xyguide.pdf