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I don't know what this double-arrow $\twoheadrightarrow$ means!

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sometimes it means surjective – Mud May 7 '13 at 13:24
It largely depends on the context and the author. I've seen it used for several things, but most often to denote a surjective mapping. – Zéychin May 7 '13 at 14:23
up vote 11 down vote accepted

From Wikipedia: Surjective funtion

A surjective function is a function whose image is equal to its codomain. Equivalently, a function f with domain $X$ and codomain $Y$ is surjective if for every $y$ in $Y$ there exists at least one $x$ in $X$ with $f(x)=y$. Surjections are sometimes denoted by a two-headed rightwards arrow, as in $f : X \twoheadrightarrow Y,\;$ [Boldface mine.]

See also the section on the properties or characterizations of "surjections".

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Time for a nice answer badge! +1 – Amzoti May 8 '13 at 0:28

This is usually used in category theory to denote an epimorphism.

Related question: Special arrows for notation of morphisms

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