Placing `\sim` above `\to`, with correct spacing

Question

In an answer to a previous question, it is explained that

\xrightarrow{\sim}

will produce an arrow pointed to the right with the \sim symbol above it (e.g., to indicate that a map is an isomorphism). However, I'm not satisfied with the spacing of this symbol, as it appears too high above the arrow:

Is there a way to move it down? Potentially the arrow would have to be widened a little, to prevent \sim from touching the arrowhead.

Answer 1

You could do this with \stackrel and \smash.

\documentclass{article}

\newcommand\isomto{\stackrel{\sim}{\smash{\longrightarrow}\rule{0pt}{0.4ex}}}

\begin{document}

$f\colon X\isomto Y$

\end{document}

Adjust the height as you wish by changing the 0.4ex. Note also the use of \colon for proper spacing of functions.

Or if you prefer a larger \sim, try

\newcommand\isomto{\stackrel{\textstyle\sim}{\smash{\longrightarrow}\rule{0pt}{0.4ex}}}

Answer 2

I add two little answers with an addendum:

1st proposal:

\documentclass{article}
\usepackage{mathtools}  
\begin{document}

\[f\colon X\overset{\raise-.5ex\hbox{$\sim$}}{\longrightarrow}Y\] 

\end{document}

2nd proposal:

Using tikz-cd package:

\documentclass[12pt]{article}
\usepackage{tikz-cd,relsize}
\tikzset{close/.style={outer sep=-1.2pt}}
\usepackage{lipsum}
\begin{document}
\lipsum[1]
\[\begin{tikzcd}[column sep=.3in]
f: X \arrow[r, close,"\mathlarger{\sim}"] & Y
\end{tikzcd}\]
\lipsum[2]
\end{document}

Addendum of the 2020/04/29: Using stix font where exists a specific symbol named \similarrightarrow. But there is an inconvenience. The stix font change the fonts of the characters and you not have the CM default font.

\documentclass[a4paper,12pt]{article}
\usepackage{mathtools,amssymb}
\usepackage{stix}
\begin{document}
\[f\colon X \similarrightarrow Y\]
\end{document}