Extendible \cong congruence sign

Question

This question is very similar to Extendible equals sign but the solutions given there do not apply immediately.

At times I woud like to clarify the nature of a mathematical congruence. So I have defined in my preamble

\newcommand*\morph[1]{\underset{\mbox{\tiny #1}}{\cong}}

So I can write things like \morph{diff} and \morph{hom} to differentiate between different congruences. But even with the \mbox content set to \tiny, the text is still wider than the congruence sign. Any ideas?

Answer 1

One could always use \resizebox to stretch the symbol.

\documentclass{article}
\usepackage{amsmath,graphicx}
\makeatletter
\newcommand*\morph[1]{%
    \setbox0=\hbox{\scriptsize#1}%
    \setbox2=\hbox{$\m@th{\cong}$}%
    \stackrel{\copy0}{%
        \ifdim\wd2<\wd0
            \resizebox{\wd0}{\ht2}{$\m@th{\cong}$}%
        \else
            \cong
        \fi
    }%
}
\begin{document}
\[X\morph{long text}Y\morph{i}Z\]
\end{document}

Answer 2

Of course, whilst agreeing that this Not Recommended, it's also fairly similar to something I do: I like to make arrows and so forth a little more conspicuous in presentation by making them a bit bigger. So my method for doing that adapts reasonably well to this situation.

That method is to use ... TikZ!

\documentclass{standalone}
\usepackage{tikz}
\usetikzlibrary{decorations.pathmorphing}

\newcommand{\xcong}[1]{%
\mathrel{\tikz[baseline=0pt] {
   \node[above] at (0,1.2ex) (a) {\(\scriptstyle #1\)};
   \draw[preaction={
      transform canvas={yshift=-.5ex},
      draw,
      decorate,
      decoration={lineto}},
     preaction={
      transform canvas={yshift=-1ex},
      draw,
      decorate,
      decoration={lineto}}]
    (a.south west) .. controls +(.25,.15) and +(-.25,-.15) .. (a.south east);
 }}}

\begin{document}
\(
A \cong B \quad A \xcong{a,b,c,d,e,f,g,h} B
\)
\end{document}

Okay, it's not going to win any design awards ...