4

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

Arrow depcting automorphism

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

  • 2
    Did you try detexify and the comprehensive symbol list? – cfr Aug 3 '16 at 2:30
  • 1
    @cfr Yes, of course! I have tried both. – Paulo Ney Aug 3 '16 at 16:56
  • It is just best to say that in your question as sometimes reviewers are a bit too trigger-happy and may close your question as a duplicate of a generic need-symbol question, which is obviously not good :(. – cfr Aug 3 '16 at 20:26
  • Do you mean automorphism or is automorphim something else? – cfr Aug 3 '16 at 20:26
  • 1
    @PauloNey Could you please add some references to books using the symbol? It will never be added to Unicode if there's no example of usage. – egreg Aug 4 '16 at 19:38
3

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}

enter image description here

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}

enter image description here

|improve this answer|||||
  • The vertical trace was just a smudge from the scan, but nice that you showed how to do even more with it the basic symbol. – Paulo Ney Aug 5 '16 at 4:37
  • @PauloNey When symbols are overlaid, the PDF rendering software (e.g. Adobe) may present them, at smaller scales, as slightly misaligned (there is no help for that). However, extreme zooming should tell whether or not the alignment is good or not. When printed out on paper, maximum printing resolution is employed and so they should print out "good". – Steven B. Segletes Aug 5 '16 at 10:45
  • I saw that! When you pull down to some 70% (a perfectly looking mix of symbols) things get smugged in a way that a normal TeX symbol does not. Do you know what the issue is with the PDF display? – Paulo Ney Aug 5 '16 at 16:01
  • It's a feature, not a bug ;^). It is called font hinting (en.wikipedia.org/wiki/Font_hinting) and it is a way for PDF viewers (and other programs that display text) to try to minimize rasterization of the image. The essential problem is that my composite is composed of three glyphs, each one of which is individually hinted by the viewer, rather than being hinted as a composite entity, which would be preferable in this case. If a font glyph existed for this symbol, it would naturally be hinted as a single character, not suffering this schizophrenia. – Steven B. Segletes Aug 5 '16 at 16:07
  • do you know the hoops of making a real glyph in a font so that would better display on an on-screen publication? That would be really worth having here. – Paulo Ney Aug 6 '16 at 1:12

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