How to redefine the colon-symbol with unicode-math (spacing problem)

Question

I want to change the usual role of : and \colon. Consider the following code

\documentclass{scrreprt}

\usepackage{amsmath}
\usepackage{unicode-math}

%\unimathsetup{colon=literal}
%\DeclareMathSymbol{:}{\mathpunct}{operators}{"3A}
%\let\colon\relax
%\DeclareMathSymbol{\colon}{\mathrel}{operators}{"3A}


\begin{document}
    \newcommand\mycolon{\mathpunct{\char"003A}}
    \newcommand\myratio{\mathrel{\char"003A}}

    \( \pi:X \to Y \) (1)

    \( \pi\myratio X \to Y \) (2)

    \( \pi\colon X \to Y \) (3)

    \( \pi\mycolon X \to Y \) (4)
\end{document}

The first two have the same gap between $\pi$ und $X$. (3) has less space and (4) the least amount. Remember the spacing of (3). Now uncomment the lines to interchange the role of ':' and \colon. Through now (1') is now correctly set as a punctation, the spacing is equal to (4') and NOT equal to the previous space of (3). Is there a way to adjust them?

EDIT: Solution due to egreg (with minimal changes)

\documentclass{scrreprt}

\usepackage{amsmath}
\usepackage{unicode-math}
\usepackage{etoolbox}


\patchcmd{\colon}{:}{\relcolon}{}{}         % Remove ':' from the definition of \colon 
\newcommand\myratio{\mathrel{\char"02236}}  % Define how the colon should look like as a ratio 
%\newcommand\myratio{\mathrel{\char"003A}}  % Use for wider space
\AtBeginDocument{
    \edef\relcolon                          % Define \recolon with current ':'
        {\mathrel{\Umathcharnum\the\Umathcodenum`:}}    
    \begingroup\lccode`~=`:                 % Make ':' math-active and redefine it to be \colon
    \lowercase{\endgroup\let~}\colon
    \mathcode`:="8000
    \let\colon\myratio                      % Redefine \colon with \myratio                      
}

\begin{document}
    \( \pi:X \to Y \) (1)

    \( \pi\colon X \to Y \) (2)
\end{document}

Answer 1

With amsmath, \colon is not simply a punctuation symbol, but has some spacing before it and more space after it than a punctuation symbol.

A (not very straightforward) way to (almost) interchange the meanings is

\documentclass{scrreprt}

\usepackage{amsmath}
\usepackage{unicode-math}
\usepackage{etoolbox}
\patchcmd{\colon}{:}{\relcolon}{}{}
\AtBeginDocument{
  \edef\relcolon{\mathrel{\Umathcharnum\the\Umathcodenum`:}}
  \begingroup\lccode`~=`:
  \lowercase{\endgroup\let~}\colon
  \mathcode`:="8000
}


\begin{document}

    \( \pi:X \to Y \) (1)

    \( \pi\mathpunct{\relcolon} X \to Y \) (2)

    \( \pi\relcolon X \to Y \) (3)

\end{document}

Case (1) is the same as \colon; case (2) is with \mathpunct to show the difference; case (3) is the colon as relation.

First of all I patch \colon so it has not an explicit : in its definition, or an infinite loop would happen. Then (at begin document), I define \relcolon with the current mathcode of : (\edef is necessary to get the explicit number). Finally I make : math active and give it the same meaning as amsmath's \colon. The usage of \relcolon in it has no consequence, because it appears braced, so considered an ordinary symbol.

However, I don't think it's a good idea to change the semantics, because it limits portability.

If you really want to use \colon for the relation, then this modification of the above code should work:

\documentclass{scrreprt}

\usepackage{amsmath}
\usepackage{unicode-math}
\usepackage{etoolbox}
\let\amsmathcolon\colon
\patchcmd{\amsmathcolon}{:}{\colon}{}{}
\AtBeginDocument{
  \edef\colon{\mathrel{\Umathcharnum\the\Umathcodenum`:}}
  \begingroup\lccode`~=`:
  \lowercase{\endgroup\let~}\amsmathcolon
  \mathcode`:="8000
}


\begin{document}

    \( \pi:X \to Y \) (1)

    \( \pi\mathpunct{\colon} X \to Y \) (2)

    \( \pi\colon X \to Y \) (3)

\end{document}

---

Note that the option colon=literal doesn't do what's requested; here's an example

\documentclass{scrreprt}

\usepackage{amsmath}
\usepackage[colon=literal]{unicode-math}


\begin{document}

    \( \pi:X \to Y \) (1)

    \( \pi\mathpunct{\colon} X \to Y \) (2)

    \( \pi\colon X \to Y \) (3)

\end{document}

So : uses a wrong spacing and \colon isn't redefined.

Answer 2

See section §5.5.6 of unicode-math documentation:

\documentclass{scrreprt}

\usepackage{amsmath}
\usepackage[colon=literal]{unicode-math}
\begin{document}

    \( \pi:X \to Y \) (1)

\end{document}