[Tex/LaTex] 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