Particular type of hook arrow

Question

Would anyone know a particular arrow in TeX that match this one, that denotes an automorphism of K?

The symbol was widely used by mathematicians in the beginning of the 20th century and is still used in certain circles.

Answer 1

Stack your own. \Hookarrowleft if you don't need it to scale to smaller math styles, or \SHookarrowleft if you do. As it is, with the \hbox as part of the definition, it can be used in text or math mode. If you only want it in math mode, you can get rid of the \hbox{$ and $} from the definition. I also did not apply any \mathbin or any such relations, because I don't know what it should be.

\documentclass{article}
\usepackage{stackengine}
\def\Hookarrowleft{\hbox{$\ensurestackMath{\stackanchor[.42pt]{%
  \scriptscriptstyle-\mkern-10mu-}{\scriptscriptstyle\leftarrow}}\mkern-6mu%
  \raisebox{1.82pt}{$\scriptscriptstyle\supset$}$}}
%% IF YOU NEED IT TO SCALE WITH MATH STYLE
\usepackage{scalerel}
\def\SHookarrowleft{\scalerel*{\Hookarrowleft}{X}}
%%
\begin{document}
$T: K \Hookarrowleft$xyz\par
$T: K \SHookarrowleft$xyz\par
$\scriptstyle T: K \SHookarrowleft$xyz\par
$\scriptscriptstyle T: K \SHookarrowleft$xyz\par
\end{document}

EDIT: If that tiny vertical strut to the left of the hook arrow in the OP's figure is part of the symbol, then it can be easily included:

\documentclass{article}
\usepackage{stackengine}
\def\Hookarrowleft{\hbox{$%
  \raisebox{1pt}{\scalebox{1}[.8]{\rotatebox{90}{$\scriptscriptstyle-$}}}\mkern-2mu%
  \ensurestackMath{\stackanchor[.42pt]{%
  \scriptscriptstyle-\mkern-10mu-}{\scriptscriptstyle\leftarrow}}\mkern-6mu%
  \raisebox{1.82pt}{$\scriptscriptstyle\supset$}$}}
%% IF YOU NEED IT TO SCALE WITH MATH STYLE
\usepackage{scalerel}
\def\SHookarrowleft{\scalerel*{\Hookarrowleft}{X}}
%%
\begin{document}
$T: K \Hookarrowleft$xyz\par
$T: K \SHookarrowleft$xyz\par
$\scriptstyle T: K \SHookarrowleft$xyz\par
$\scriptscriptstyle T: K \SHookarrowleft$xyz\par
\end{document}