how to automatically permit hyphenation of the word "category" in "$\infty$-category"

Question

The word category gets automatically hyphenated as cate-gory by latex, but with the prefix $\infty$-, it doesn't. It still works by manually writing $\infty$-cate\-gory, but putting \hyphenation{$\infty$-cate-gory} in the preamble apparently gets ignored by lualatex, and gives an error message with pdflatex.

Is there a way to automate the hyphenation of words with math prefixes like $\infty$-category?

EDIT:

Here is something that works that I found on the arxiv. But it forces me to write something else instead of the usual hyphen, and I would prefer a solution where I can just write an ordinary hyphen.

\documentclass{article}
\usepackage[shortcuts]{extdash}
\newcommand\oo[1]{$\infty$=/}
\begin{document}
This is a sufficiently long line of text with many words 
and ending in \oo-category.
Or without the newcommand:
This is a sufficiently long line of text with many words 
and ending in $\infty$=/category.
\end{document}

Answer 1

Not really an answer, and I am afraid it might not help you, but too long for a comment, and it might help someone else.

I wonder if there is a simple and clean way to do this in pdftex or luatex. In luametatex, a more flexible hyphenation setup is implemented. One can use \hyphenationmode (see the luametatex manual) to set it up (or use the defaults that seem to work well). In lang-ini.mkxl, in a ConTeXt distribution, one can find something like

\permanent \integerdef \completehyphenationcode \numexpr
    \normalhyphenationcode            % \discretionary
  + \automatichyphenationcode         % -
  + \explicithyphenationcode          % \-
  + \syllablehyphenationcode          % pattern driven
  + \uppercasehyphenationcode         % replaces \uchyph
  + \compoundhyphenationcode          % replaces \compoundhyphenmode
  % \strictstarthyphenationcode       % replaces \hyphenationbounds (strict = original tex)
  % \strictendhyphenationcode         % replaces \hyphenationbounds (strict = original tex)
  + \automaticpenaltyhyphenationcode  % replaces \hyphenpenaltymode (otherwise use \exhyphenpenalty)
  + \explicitpenaltyhyphenationcode   % replaces \hyphenpenaltymode (otherwise use \exhyphenpenalty)
  + \permitgluehyphenationcode        % turn glue into kern in \discretionary
  + \permitallhyphenationcode         % okay, let's be even more tolerant
  + \permitmathreplacehyphenationcode % and again we're more permissive
  + \forcehandlerhyphenationcode      % kick in the handler (could be an option)
  + \feedbackcompoundhyphenationcode  % feedback compound snippets
  + \ignoreboundshyphenationcode      % just in case we have hyphens at the edges
  + \collapsehyphenationcode          % collapse -- and ---
\relax
\permanent \integerdef \partialhyphenationcode \numexpr
    \ignoreboundshyphenationcode      % just in case we have hyphens at the edges
% + \explicithyphenationcode          % -

\collapsehyphenationcode          % collapse -- and ---

\relax
\permanent\protected\def\dohyphens {\hyphenationmode\completehyphenationcode}
\permanent\protected\def\nohyphens {\hyphenationmode\partialhyphenationcode}

Hyphenations are on by default, but following the code above, we can switch them off by \nohyphens. Of course, one can have a more granular setup as well by setting the different bits (one can switch one with \bitwiseflip).

Here is a small example where we change the hyphenation setting locally (to prohibit the wanted hyphenation, therefore in red):

\starttext
% \showhyphens{category}
\typ{\showhyphens{category}}
\typ{languages       > hyphenation > show: cat[-||]e[-||]gory}
\blank
\hsize 1.4cm
\blackrule[width=\hsize]\par
$\infty$-category
\blank
\hsize 7cm
\blackrule[width=\hsize]\par
Oh, it's like that, it's like that {\red\nohyphens$\infty$-category.}
Yeah, it's like that, it's like that $\infty$-category. Woah-oh-oh, oh-oh-oh.
\stoptext