After loading unicode-math, how do I remap one symbol (character) to another?

Question

I specifically want "⦂" (U2982, Z NOTATION TYPE COLON) to appear as a colon with mathrel spacing (or better yet, the way amsmath redefines \colon)

But redefining \typecolon with \AtBeginDocument doesn't work. I have also tried using lower level unicode-math commands. A MWE containing my attempts follows:

%!TEX program = lualatex

\documentclass{article}
\usepackage[math-style=ISO, partial=upright]{unicode-math}
\setmathfont{LibertinusMath-Regular.otf}

\AtBeginDocument{
  \let\typecolon\colon % fails
% \renewcommand{\typecolon}{\nobreak\mskip2mu\mathpunct{}\nonscript
% \mkern-\thinmuskip{:}\mskip6muplus1mu\relax} % fails
}

% \ExplSyntaxOn
% \AtBeginDocument{
  % \__um_process_symbol_noparse:nnn {"02982}{:}{\mathrel} % fails
  % \__um_process_symbol_noparse:nnn {"02982}{\colon}{\mathrel} % fails
  % \__um_remap_symbol:nnn {\`⦂} {\mathrel} {"02236} % fails
  % \__um_remap_symbol:nnn {\typecolon} {\mathrel} {"02236} % fails
% }
% \ExplSyntaxOff


\begin{document}

With explicit symbol: $f ⦂ A → B.$

With \verb|\symbol|: $f \symbol{"02982} A → B.$

With \verb|\typecolon|: $f \typecolon A → B.$

\end{document}

Which results in

My assumption was that unicode-math defines the bare unicode character is defined as an ‘active character’ which expands to \typecolon, as per unicode-math-table.tex but, obviously, I'm wrong or redefining \typecolon would work.

What is the correct approach here? And where is my misunderstanding? Thanks in advance for all replies.

---

Version details:

I am using LuaLaTeX with unicode-math:

>_ lualatex --version                       
This is LuaHBTeX, Version 1.14.0 (TeX Live 2022/dev/Debian) […]

Specifically, that which is packaged with Ubuntu 22.04.

Answer 1

Assigning a \mathcode of "8000 makes a character “math active”. When used in math mode, such a 〈character〉 is replaced by an active character token having the original character code (TeXbook p. 289). Therefore, we only have to assign the appropriate \mathcode and make it so that the active ⦂ behaves as \colon.

% Tested with LuaTeX and XeTeX
\documentclass{article}
\usepackage[math-style=ISO, partial=upright]{unicode-math}
\setmainfont{STIX-Regular.otf}  % to show the ⦂ in horizontal mode
\setmathfont{LibertinusMath-Regular.otf}

% In LuaTeX, \letcharcode`⦂=\colon can replace the following line (Marcel Krüger's hint)
\begingroup \lccode`~=`⦂ \lowercase{\endgroup\def~}{\colon}
\AtBeginDocument{\mathcode`⦂="8000\relax}

\begin{document}

With \verb|\colon|: $f \colon A → B$.

With explicit symbol: $f ⦂ A → B$.

With \verb|\symbol|: $f \symbol{"02982} A → B$.

“⦂” is still “\symbol{"02982}” (\verb|\symbol{"02982}|) in horizontal mode.

\end{document}

In math mode, \symbol{"02982} is also replaced by the active ⦂, because it expands to \char"02982\relax, and \char"02982 is a 〈character〉 that is treated in the same way in math mode as ⦂-with-catcode-12 (TeXbook p. 289).

Answer 2

Just to point out the "internal unicode-math API" option, which the OP appears to prefer:

\documentclass{article}
\usepackage[math-style=ISO, partial=upright]{unicode-math}
\setmainfont{STIX-Regular.otf}
\setmathfont{LibertinusMath-Regular.otf}

\ExplSyntaxOn
\AtBeginDocument{
 \__um_mathactive_remap:nn {"2982} {\colon}
}
\ExplSyntaxOff

\begin{document}

With \verb|\colon|: $f \colon A → B$.

With explicit symbol: $f ⦂ A → B$.

With \verb|\symbol|: $f \symbol{"02982} A → B$.

“⦂” is still “\symbol{"02982}” (\verb|\symbol{"02982}|) in horizontal mode.
% MWE copied from the other answer, I don't actually have the fonts to test but testing with default font works well
\end{document}

In some other versions I think you need to drop the first __? _{as expected of an internal API.}

There's also the \__um_map_char_single:nn and such under section "15.1   Mapping 'naked' math characters" in unicode-math-code.pdf but the documentation is a bit dense...