Arrow with a loop in the middle

Question

I'm looking for a symbol for an arrow whose shaft "goes through a loop" in the middle. Ideally the arrow should be just like a normal arrow symbol with a straight shaft, but in the middle it "curls" into a loop that ends on the same height as it began. Then the shaft continues until it ends in the head. Is there a symbol at least somewhat like this (I checked the comprehensive symbol list and couldn't find one)? If not, I thought about making one by putting a horizontally inverted $\hookrightarrow$ symbol together with a straight $\hookrightarrow$, so that the hooks assemble into a loop, but I would have to cut out some of the length of the arrows so that the composite isn't way too long. Is there a way I can do that?

Answer 1

Like this?

\documentclass[border=3mm]{standalone}
\newcommand{\rightlooparrow}{\mathbin{
    \vbox{\openup-10.25pt\halign{\hss$##$\hss\cr\circ\cr\longrightarrow\cr}}
}}
\begin{document}
$A \rightlooparrow B$
\end{document}

If you want it to work in different sizes (subscript etc) you would need to make a mathpalette version.

Answer 2

You can smash a bit the circle. The following also works in all math styles.

\documentclass{article}
\usepackage{amsmath}
\usepackage{graphicx}

\makeatletter
\newcommand{\smashed@circ}{\mathpalette\smashed@@circ\relax}
\newcommand{\smashed@@circ}[2]{%
  \scalebox{1}[0.5]{$\m@th#1\circ$}%
}

\newcommand{\loop@arrow}[3]{%
  \mathrel{\mathpalette\loop@@arrow{{#1}{#2}{#3}}}%
}
\newcommand{\loop@@arrow}[2]{\loop@@@arrow#1#2}
\newcommand{\loop@@@arrow}[4]{%
  \ooalign{%
    \loop@raise{#1}%
    \hidewidth\raisebox{\loop@raise@amount}{$\m@th#1#3\smashed@circ#4$}\hidewidth\cr
    $\m@th#1#2$\cr
  }%
}
\newcommand{\loop@raise}[1]{%
  \settowidth\dimen@{$\m@th#1\mspace{1mu}$}%
  \edef\loop@raise@amount{%
    \ifx#1\displaystyle\the\dimexpr4\dimen@\else
    \ifx#1\textstyle\the\dimexpr4\dimen@\else
    \ifx#1\scriptstyle\the\dimexpr3.5\dimen@\else
    \the\dimexpr3\dimen@\fi\fi\fi
  }%
}
\newcommand{\looprightarrow}{\loop@arrow{\rightarrow}{\!}{}}
\newcommand{\loopleftarrow}{\loop@arrow{\leftarrow}{}{\!}}
\newcommand{\looplongrightarrow}{\loop@arrow{\longrightarrow}{\!}{}}
\newcommand{\looplongleftarrow}{\loop@arrow{\longleftarrow}{}{\!}}
\makeatother

\begin{document}

$A\looprightarrow B$
$\scriptstyle A\looprightarrow B$
$\scriptscriptstyle A\looprightarrow B$

$A\looprightarrow B\loopleftarrow C$

$A\looplongrightarrow B\looplongleftarrow C$

\end{document}