Commonly used arrows with TikZ

Question

In a previous question Gonzalo Medina and Peter Grill gave a solution to replace the \to arrow by an arrow generated by TikZ.

For some people using TikZ in commutative diagrams, it would be perhaps desirable to uniformize the tips of some common arrows (\to, \leftarrow, \mapsto,\rightsquigarrow,etc.)

One can extend Peter Grill's solution in the question above (Gonzalo Medina's solution provides an arrow that resizes, but since arrows other than \to are less commonly used in super- or subindices, here the simplest solution is used) to obtain a\leftarrow as in the code show bellow. The problem is with the \mapsto arrow, for I cannot produce it: its vertical part is too large, as shown in the picture bellow.

\documentclass{article}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsmath}

% Tikz part
%********************************************************************
\usepackage{tikz}
\usetikzlibrary{mindmap,trees}
\usetikzlibrary{arrows,chains,matrix,positioning,scopes}
\makeatletter
\tikzset{join/.code=\tikzset{after node path={%
\ifx\tikzchainprevious\pgfutil@empty\else(\tikzchainprevious)%
edge[every join]#1(\tikzchaincurrent)\fi}}}
\makeatother
%
\tikzset{>=stealth',every on chain/.append style={join},
         every join/.style={->}}
\tikzstyle{labeled}=[execute at begin node=$\scriptstyle,
   execute at end node=$]
\usepackage{tikz-cd}
\usetikzlibrary{arrows}
\tikzset{
commutative diagrams/.cd,
arrow style=math font,
diagrams={>=stealth}} 
%*******************************************************
%redefining the arrows
%*******************************************************
\newcommand{\MyOt}[1][]{\mathbin{\tikz \draw [#1, stealth-] (0,0) (0,0.5ex) -- (1.0em,0.5ex);}}
\newcommand{\MyTo}[1][]{\mathbin{\tikz \draw [-stealth, #1] (0,0) (0,0.5ex) -- (1.0em,0.5ex);}}
\newcommand{\MyMapsto}[1][]{\mathbin{\tikz \draw [|-stealth, #1] (0,0) (0,0.5ex) -- (1.0em,0.5ex);}}

\let\OldTo\to
\let\OldOt\leftarrow
\let\OldMapsto\mapsto
\renewcommand{\to}{\MyTo}%
\renewcommand{\leftarrow}{\MyOt}
\renewcommand{\mapsto}{\MyMapsto}
\newcommand{\where}{\quad\mbox{where}\quad}
%************************************************** 

\begin{document}    

\begin{align*}
f: A\to B & \quad \rightsquigarrow \quad f^*:A^*\leftarrow B^*\where  f^*:\phi \mapsto \phi\circ f\qquad&\mbox{(with TikZ)} \\
f: A\OldTo B &\quad \rightsquigarrow \quad f^*:A^*\OldOt B^* \!\!\where f^*:\phi \OldMapsto \phi\circ f\qquad &\mbox{(ordinary)}\\
\end{align*}

\end{document}

The result is:

Answer 1

Does this help? I put together a composite \mapsto, by adding a vertical rule to a stealth arrow (outside of tikz) EDIT: Now it works in \scriptstyle

\documentclass{article}
% See http://tex.stackexchange.com/questions/14386/importing-a-
%            single-symbol-from-a-different-font
% Setup the matha font (from mathabx.sty)
\DeclareFontFamily{U}{matha}{\hyphenchar\font45}
\DeclareFontShape{U}{matha}{m}{n}{
      <5> <6> <7> <8> <9> <10> gen * matha
      <10.95> matha10 <12> <14.4> <17.28> <20.74> <24.88> matha12
      }{}
\DeclareSymbolFont{matha}{U}{matha}{m}{n}

% Define a subset character from that font (from mathabx.dcl)
% to completely replace the \subset character, you can replace
% \varsubset with \subset

\DeclareMathSymbol{\varleftarrow}{3}{matha}{"D0}
\DeclareMathSymbol{\varrightarrow}{3}{matha}{"D1}

\usepackage{scalerel}

\def\Newmapsto{%
  \mbox{$\displaystyle\rule{.3ex}{0ex}\rule[.2ex]{.075ex}{.8ex}\rule{-.8ex}{0ex}%
  \varrightarrow$}}%
\def\newmapsto{%
\scalerel*{\Newmapsto}{\scaleobj{1.2}{\mapsto}}%
}
\begin{document}
\[
A \mapsto B \qquad A \newmapsto B \scriptstyle \qquad 
A \mapsto B \qquad A \newmapsto B
\]
\end{document}

---

Thanks to varsop for the very effective and simpler alternative using \joinrel:

\documentclass{article}
% See http://tex.stackexchange.com/questions/14386/importing-a-
%            single-symbol-from-a-different-font
% Setup the matha font (from mathabx.sty)
\DeclareFontFamily{U}{matha}{\hyphenchar\font45}
\DeclareFontShape{U}{matha}{m}{n}{
      <5> <6> <7> <8> <9> <10> gen * matha
      <10.95> matha10 <12> <14.4> <17.28> <20.74> <24.88> matha12
      }{}
\DeclareSymbolFont{matha}{U}{matha}{m}{n}

\DeclareMathSymbol{\varleftarrow}{3}{matha}{"D0}
\DeclareMathSymbol{\varrightarrow}{3}{matha}{"D1}
\DeclareMathSymbol{\mapstochar} {3}{matha}{"DE} 
\def\newmapsto{\mapstochar\joinrel\kern1.7pt\varrightarrow}

\begin{document}
\[
A \mapsto B \qquad A \newmapsto B \scriptstyle \qquad 
A \mapsto B \qquad A \newmapsto B
\]
\[
\scriptscriptstyle A \mapsto B \qquad A \newmapsto B
\]
\end{document}