Special Symbol "::="

Question

As the title says, does LaTeX have this special symbol:

::=

I tried to look at some cheat-sheets and http://detexify.kirelabs.org/classify.html but could not find it.

Answer 1

Yes, it is called \Coloneqq and it's defined by the mathtools package, which is an extension of amsmath.

MWE

\documentclass{article}
\usepackage{mathtools}

\begin{document}
\[
\Coloneqq
\]
\end{document} 

The package also provides other symbols like the above one (see subsubsection 3.7.3 of the documentation) including \vcentcolon which is a colon properly vertically centered.

Moreover, issuing

\mathtoolsset{centercolon}

you can have all your math colons (including the \colon command) properly vertically centered.

Example:

\documentclass{article}
\usepackage{mathtools}
\mathtoolsset{centercolon}

\begin{document}
\[
\colon \quad : \quad \coloneqq \quad \Coloneqq
\]
\end{document} 

Answer 2

Package colonequals provides such symbols with properly vertically centered colons:

\documentclass{article}
\usepackage{colonequals}

\begin{document}
\[ A \coloncolonequals B \]
\end{document}

OpenType fonts

If the TeX engine supports OpenType fonts (LuaTeX, XeTeX), then the symbol can be used directly as Unicode symbol ⩴ (U+2A74) or macro \Coloneq, if package unicode-math with a font, which contains this symbol.

When testing fonts, \tracinglostchars=2 is useful, because then missing characters are also logged on the screen, e.g.:

Missing character: There is no ⩴ (U+2A74) in font "[latinmodern-math]:mode=base;script=math;language=DFLT;"!

Asana-Math

\documentclass{article}
\usepackage{unicode-math}
\setmathfont{Asana-Math.otf} 
\begin{document}
  \[ A \Coloneq B \]
\end{document}

XITS Math

\setmathfont{xits-math.otf}

Answer 3

If you needn't to use any packages, you can define the symbol:

\def\cceq{\mathrel{\vcenter{\hbox{::}}{=}}}

$$ A \cceq B $$
\bye