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I'm wondering what muglue means in LaTeX and what it is an abbreviation/acronym of: m/u/glue. I have some idea though what glue in LaTeX means.

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From The TeXbook (my emphasis):

[. . .] they are defined in terms of muglue, a special brand of glue intended for math spacing. You specify muglue just as if it were ordinary glue, except that the units are given in terms of mu (math units) instead of pt or cm or something else.

As requested, also from The TeXbook:

Dangerous bend There are 18 mu to an em, where the em is taken from family 2 (the math symbols family). In other words, \textfont 2 defines the em value for mu in display and text styles; \scriptfont 2 defines the em for script size material; and \scriptscriptfont 2 defines it for scriptscript size.

which means that a mu unit is computed from the current math symbols font, which respects the current math style (i.e., a mu unit is smaller in subscripts and even smaller in sub-subscripts), this is what makes it ideal for use in math: the spacing will be proportional, so to speak, to the font size.

Also, both LaTeX and Plain TeX define these quantities in terms of mu units:

\thinmuskip = 3mu % \,
\medmuskip = 4mu plus 2mu minus 4mu % \>
\thickmuskip = 5mu plus 5mu % \;
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  • You might want to add that mu depends on the current font, as it is 1/18 em, and that, for instance, \thinspace is 3mu.
    – Bernard
    Oct 17, 2019 at 12:23
  • @Bernard It corresponds to 1/18 em in the symbol font (family 2) of the current math style.
    – egreg
    Oct 17, 2019 at 12:25
  • @egreg: Thank you for this clarification!
    – Bernard
    Oct 17, 2019 at 12:27
  • @Bernard Done :-) (actually, that's \thinmuskip; \thinspace is a \kern .16667em in text-mode) Oct 17, 2019 at 12:32

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