What does the notation $\twoheadrightarrow$ mean?

Question

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

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 07 '13 at 14:23

score 12 · Accepted Answer · answered May 07 '13 at 13:31

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".

Time for a nice answer badge! +1 – Amzoti May 08 '13 at 00:28 — Amzoti, May 08 '13 at 00:28

score 11 · Answer 2 · edited Apr 13 '17 at 12:20

11

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

Related question: Special arrows for notation of morphisms

edited Apr 13 '17 at 12:20

Community

1

answered May 07 '13 at 13:25

FiveLemon

358

What does the notation $\twoheadrightarrow$ mean?

2 Answers2