A very simple question, I just totally forgot how it was called, and google is not helping.

There's a pair of functions $f:X\to Y$, $g:Y\to X$.

$fgf = f$, $gfg = g$, but $fg$ and $gf$ don't need to be identities (and usually are not in interesting cases).

A simple example would be $f(a,b,c)=(a,b)$, $g(a,b)=(a,b,0)$

What were $f$ and $g$ called?