DEF-SUR. Surjection.
A surjection / onto function is a function $f:X\to Y$ that is surjective, i.e. for all $y\in Y$ there is an $x\in X$ such that $f(x)=y$. In other words, $\operatorname{ran}f=Y$.
REM-SUR.
Notice that surjectivity of a function is not an intrinsic property, since the codomain is not intrinsic (REM-F-COD).
We can make every function surjective by choosing its range as its codomain.