DEF-BIJ. Bijection.
A bijection / one-to-one correspondence is a function that is both an injection and an surjection, i.e. an injection $f:X\to Y$ such that $\operatorname{ran}f=Y$.
REM-BIJ.
Since surjectivity is not an intrinsic property (REM-SUR), nor is bijectivity.
We can make every injection a bijection by choosing its range as its codomain.